Obtaining accurate displacement measurements for large material deformation and/or rotation presents a distinct challenge to digital image correlation (DIC) due to cumulative and decorrelation errors, particularly near material boundaries.We aim to accurately measure the deformation gradient tensor near boundary discontinuities in situations of large deformation and large deformation gradients.To achieve this goal, the locations of randomly distributed particles are tracked using an open-source particle-tracking software, Trackpy. A least-squares estimate of the deformation gradient tensor field uses nearest-neighbor material vectors and a first-order Finite Difference (FD) approximation, circumventing common errors in other methods. The error caused by FD approximation and that incurred by measurement are derived and tested with exhaustive numerical simulations. Furthermore, a uniaxial tensile test and mode-I fracture experiment are conducted with particle-embedded hydrogels to validate the method.Numerical results corroborate a theoretical expression of measurement error. They show that the FD error increases while the measurement error decreases for a growing estimating radius. Moreover, measurement error is linearly correlated to displacement noise. A benchmark uniaxial tensile test validates the accuracy of the proposed estimator, and the near-crack-tip measurements in a tensile fracture experiment demonstrate the estimator’s capabilities near a free surface, when a material undergoes large deformation and rotation. The results of the displacement and strain data are benchmarked against kinematic data obtained using an open-source DIC software, Ncorr. Computation time for both methods is compared.A deformation gradient tensor estimator is developed based on a particle tracking technique and a least squares routine. Theoretical error bounds on the estimator are verified by numerical simulations, and the method’s capability is confirmed by physical experiments in evaluating large deformation and rotation near a free boundary. The proposed estimator is expected to open a door towards future material tests and experimental mechanics studies, especially in large deformation and large rotation scenarios. Material deformation is the most essential kinematic process in solid mechanics, and its quantification remains a cornerstone of experimental mechanics. From the point-wise strain gauge  to stateastomers  or hydroastomers , 5. \docn states , 8.In order to quantify mentclass2pt{minimmentclasspt{minimamentclasspt{minimaIn DIC, displacement data is obtained at gridded points by correlation of pixel subsets in speckle images before and after deformation. In order to obtain the displacement data, a warping vector consisting of stretches, shears and rigid translations is often used to optimize the correlation; however, oftentimes, rotation of a subset is not included in the warping vector. This may generate inaccuracies in the measured displacement data. Nevertheless, the grid format of displacement measurements enables elementary gradient computations with finite difference methods, rendering the calculation of nd shape . In ordend shape , polar cnd shape , a defornd shape , quasi-cnd shape , scale-ind shape –23, and nd shape , 25. Amond shape . Incremend shape , 27, butnd shape  or shearnd shape . Althougnd shape , 31, subnd shape , 32, andnd shape –35 have As an alternative to DIC, particle tracking measures displacement fields via dispersed particles. While this method is less popular, it inherently avoids the subset decorrelation and splitting problems in DIC, and enables reliable evaluation of large deformation and large rotation, especially near free surfaces. When correctly implemented, it can be highly accurate, achieving sub-pixel resolution of the particle positions –44. BaseMost developments and applications of particle tracking in the last three decades are found in biophysics , 49–51, k-nearest neighbors . The particle images are first pre-processed by a bandpass filter to suppress image noise and to remove any large structures, which might be falsely detected as a particle during the tracking process. The filtered images are then used as inputs for the open-source particle tracking algorithm, Trackpy , which aA uniaxial tensile test is conducted first to verify accuracy of the proposed estimator since the displacement field and deformation gradient tensor are well known for linear elastic solids under the assumption of small strains as:mentclass2pt{minimWhile loading the sample, particle images are recorded at each strain increment. By tracking the particles before and after deformation, the displacement fields are measured, e.g., the displacement component along the loading direction, equation  using a k. The relative error between k, and compared to the theoretical measurement error in equation (k from 5 to 100, which may arise due to the least squares fit of displacement, or due to inaccuracies in the measurement of the reference state. Furthermore, the relative error is found to decrease at a rate of k due to the finite domain size. The R is related to k via the 2D particle density k limit results from the finite size of the domain. Nevertheless, a degree of consistency is established between theory and experiment, and effectiveness of the estimator proposed in equation (The deformation gradient tensor, entclass1pt{minimaequation , and is entclass1pt{minimaOur proposed estimator was also used to measure the deformation gradient near a mode I crack tip, where large deformation and rotation occur. The experiment is carried out with the same experimental setup depicted in Fig. Therefore, the displacement fields are accurately retrieved, and the displacement component along the loading direction, Using our deformation gradient estimator given by equation , the def uniform . Here, dThe Eulerian-Almansi finite strain tensor, The time consumed for particle tracking, particle linking, and In general, the particle locating and Hundreds of seconds are required to calculate the full-field deformation gradient tensor for 251 frames. In contrast to DIC, particle tracking generally requires a higher frame rate, especially in our fracture experiment, where the displacement can be large near the crack tip. To obtain the DIC results shown in Figs. The DIC implementation used in this manuscript is carried out with open-source software, Ncorr . Since tWe further apply particle tracking to 3D displacement measurement in a uni-axially stretched hydrogel sample, and extend our proposed estimator to 3D in order to estimate The particles are randomly distributed in the recorded volumetric image. Despite the sphericity of the particles, they appear as elongated ellipses in the images, with the major axis oriented parallel to the Despite the deficiency of the imaging system’s illumination scheme, particles are robustly located and linked in 3D by Trackpy  for a toentclass1pt{minimaAlthough the estimator given by equation  can be sk. For instance, to ensure invertibility, k must be larger than the number of spatial dimensions. Nevertheless, even when k is relatively small, neighbors could be closely aligned with high probability, leading to poor SNR of the displacement variation along certain directions. The noise in the estimated deformation gradient would be amplified along these directions, as a consequence of the small minimal eigenvalue of k increases, neighbors are less and less likely to be aligned; as a consequence, richer measurements of displacement variation are more probable, leading to a better eigenvalue distribution of k increases. Error also decreases due to an increasing smallest eigenvalue before approaching an asymptotic limit.The theoretical description of expected error in equation  gives inequation  which coThe proposed estimator is developed based on the particle tracking method. Both the particle tracking and DIC methods can realize non-contact, full-field displacement measurement with similar computational cost, and can be extended to 3D measurements, depending on the imaging system. Indeed, DIC has become more popular than particle tracking in experimental solid mechanics, thanks to its gridded data format. With the proposed estimator, non-gridded data is no longer a problem for estimating ormation , 27. Morormation . Third aormation , where sJ-integral [More attention is advocated for the deformation gradient tensor. In the wide application of experimental methods to the measurement of deformation, strain tensors are used extensively; however, deformation cannot be fully described by the strain tensors. For example, in the previously described fracture experiment, material rotation is measured to be more than cument}F , which ocument}F , 66, reqintegral , 68, alsk, before reaching a nonzero asymptotic limit. As for measurement error, numerical simulations boast a In this manuscript, a technique for estimating the deformation gradient is developed and analyzed based on a set of randomly dispersed displacements measured by particle tracking. The deformation gradient estimator given by equation  is deriv


Chickpea flour, which is produced in various forms, has high protein and fiber content; therefore, it can be a good ingredient for gluten-free cookies. The objective of this study was to investigate and compare the properties of cookies formulated using raw (RCF), cooked (CCF), and germinated (GCF) chickpea flours. The techno-functional properties of these flours were determined, and scanning electron microscope images and mid-infrared spectra were obtained. The rheological properties of cookie doughs were measured along with their mid-infrared spectra. Baked cookies were analyzed for their technological properties as well as their in vitro digestion properties. Sensory analysis was also performed for all the cookies. The most significant difference among the flours was observed in their water retention capacity, and CCF had 119.7% higher water retention capacity compared to RCF. The dough made with CCF had quite different rheological properties from the others. The cookies baked with GCF had the highest baking loss and spread ratio. The CCF-containing cookies had the hardest structure. The cookies made from RCF had a higher resistant starch content followed by the cookies with GCF. All the cookies had similar scores in all aspects tested in the sensory analysis. The use of three different forms of chickpea flour in cookie formulations resulted in products with very different properties; however, their overall acceptability levels were close. The gluten-free product market, in which bakery products have a sizable share, has a value of around USD 5.6 billion, and it is estimated to reach USD 8.3 billion by 2025 . There aCicer arietinum L.) holds considerable significance as a prominent member. The chemical compositions of legumes and their flours are balanced in terms of protein, carbohydrates, and dietary fibers, and they have a low glycemic index [Replacing gluten in food products is a difficult task due to various issues, including nutritional gaps and challenges related to maintaining the desired texture. Legume flours such as chickpea flour can become good alternatives in gluten-free bakery products due to their compositional properties. Legumes have an important role in the human diet due to their nutritional value, and the chickpea  and germinated (GCF) chickpea flours were obtained from Ingro , and cooked chickpea (CCF) flour was purchased from Naturelka .The moisture, fat, protein, and ash contents of the flours were determined according to AOAC methods 925.05, 960.39, 950.48, and 923.03, respectively. The carbohydrate contents were calculated as 100%—total% of other compounds. The crude fiber contents were determined using the AOAC method 14.020. The total phenolic contents of the flours were measured using a spectrophotometric method in the literature, and the results were expressed as mg gallic acid equivalent/L . The valL*, a*, and b* values were performed with a colorimeter . Bulk density was determined following a procedure in the literature [−1 resolution. Air spectra were obtained as the background before each measurement. Five measurements were taken from each flour type.Color measurements for the terature . AACC Meterature . MicroscThe cookie formulations included 90 g of either raw, cooked, or germinated chickpea flour. The other ingredients were the same for all the cookies, and they were 1 egg (~60 g), 10 g corn starch , 60 g margarine , 40 g brown sugar , and 10 g baking powder . All the ingredients were blended in a mixer , and 20 g of dough was shaped with a round mold of 5 cm diameter. Then, the cookie doughs were baked in a convection oven  at 175 °C for 10 min. Two batches with 10 cookies/batch were prepared from each type.Dough rheology was analyzed with a back extrusion technique using a texture analyzer  with a 25 mm cylinder probe (P/25), and the parameters were set at a pre-test speed of 2 mm/s, a test speed of 3 mm/s, a post-test speed of 10 mm/s, and a trigger force of 50 g. A standard-size back extrusion cylindrical container  and a back extrusion rig (model A/BE) were used. The container was filled with 50 g of cookie dough. A probe penetrated to a depth of 20 mm and then returned to the starting position. The measurement parameters were chosen according to the values given in the database of the equipment, with slight modifications. The cohesiveness and viscosity index values were calculated from the back extrusion profile curve . Two mea−1 resolution. Air spectra were obtained as the background before each measurement. Five measurements were taken from each batch.Mid-IR spectra of the cookie doughs were obtained with the attenuated total reflectance (ATR) accessory of the FTIR spectrometer . The doughs were placed on ZnSe crystal, and 96 scans were taken at a 4 cmThe diameters and thicknesses of 10 baked cookies per cookie batch were measured with a caliper, and the averages were calculated. The spread ratio of the cookies was calculated by dividing the diameter of the baked cookie by its height . The moiTextural properties were determined using a texture analyzer , and the hardness value was obtained via a 3-point bending test using a 3-point bending rig, with a trigger force of 5 g and a load cell of 5 kg. Also, the pre-test speed of 1.5 mm/s, test speed of 2.0 mm/s, post-test speed of 10 mm/s, and distance of 10 mm were used as measurement parameters, and the distance between the two bottom supports was adjusted to 50 mm. The peak value of the force was recorded as hardness when the cookies were broken into two pieces . MeasureTheoretical nutritional values were calculated from the ingredients according to Atwater’s calorie values, as given in Equation (1):2SO4 was added into each cell; then, the absorbance of the samples was measured at 540 nm (37 °C). The values were the averages of 6 measurements.For in vitro digestion analysis, the nutritionally significant starch components in the gluten-free cookies were determined according to a procedure in the literature . SamplesFor the sensory analysis, 38 untrained participants  evaluated 3 types of cookies for their color, flavor, texture, taste, and overall acceptability in a hedonic 1–7 scale , which is an affective type of sensory test. The sensory panel was conducted in a sensory evaluation laboratory. Individual panel booths that were lit with white light were used during testing. Each sample of the cookies was coded with a distinct number and placed on white plastic plates. The panelists were also given a glass of water to rinse their palates. The sensory study was approved by the Izmir Institute of Technology Scientific Research and Publication Ethics Committee (Number: 19.09.2022-E.96273).p <  0.05).The results were evaluated by analysis of variance (ANOVA) using Minitab  and Tukey’s pairwise comparison test to obtain differences between individual types for different properties  and GCF (0.74 g/mL) had higher bulk density compared to RCF (0.1 g/mL). It has been reported that the bulk densities of several chickpea cultivars have a variation from 0.536 g/mL to 0.571 g/mL , which aAmong the functional properties, the most significant difference was observed in the water retention capacity of the flours; CCF had the highest average value (300.76%), and RCF had the lowest (137.26%). Therefore, CCF had about 2.2 and 1.73 times higher water retention capacity than RCF and GCF, respectively. Water retention capacity is an important techno-functional property for baking applications and can be related to the rheological properties of the dough. In the previous studies, higher oil absorption and water absorption capacities were recorded for the flours from the germinated and the cooked chickpeas ,39, and −1 and 1100–950 cm−1 regions of the CCF spectra had differences in some small peaks with respect to the other types, and these small peaks present in the other two flours with the aforementioned wavenumbers disappeared in the CCF spectra. The 1500–1400 cm−1 region is attributed to the peaks due to the -CH2 and C-OH deformations for carbohydrates, and the 1100–1000 cm−1 area belongs to the fingerprint region and is mostly associated with carbohydrates [The FTIR spectra of the flours were visually inspected to determine the differences in the peaks that were associated with the chemical bonds a. The sphydrates .2: 0.98–0.99) were obtained when the water retention capacity versus all the measured rheological properties was plotted. As all the plots could be constructed with only three points representing each flour, this conclusion should be treated cautiously. CCF, with higher water retention capacity, caused the formation of doughs with higher values of the rheological properties, and this can be attributed to the gelatinization of starch during the cooking of the chickpeas, which is evident from the SEM images and FTIR spectra of the flours. There were some handling problems during the cookie preparations, and the cookie doughs made with RCF and GCF were too sticky to work with. It was very difficult to shape them using a cookie cutter. These observations also confirm the differences among the cookies made with the different flour types.The rheological parameters obtained from the back extrusion measurement of the dough prepared using CCF were significantly different from the doughs made with RCF and GCF . The pea−1, corresponding to the carbohydrate region with C-O stretching and C-O-C asymmetric stretching [The FTIR spectra of the doughs prepared from the three types of flour are presented in retching . This isThe baked cookies were analyzed for their physical and functional properties, and RCF produced the hardest cookies (7.91 N), and the hardness values of the cookies containing CCF (5.03 N) and GCF (4.72 N) were not statistically different from each other . The cooL* and b* values (L* values, while the cookies containing RCF had the highest b* value. The a* values of the RCF and GCF cookies were very close; however, CCF resulted in the cookies having significantly different a* values. In another study, it was also observed that cookies made from germinated pinto flour had a significantly lower L value compared to raw and cooked pinto flour-containing cookies [For the bakery products, color is one of the important features that affect the consumers’ perception of the product. The color analysis indicated that all the cookies had significantly different * values . The coo cookies . The dif cookies . Figure The in vitro digestion behaviors of the cookies made with three different chickpea flours were also investigated. The nutritional values of the cookies were calculated theoretically using the compositional data and Atwater’s calorie constants and are listed in The sensory analysis indicated that the overall acceptability of all the cookies was similar . In geneWhile the majority of the crucial parameters that defined the techno-functional and digestibility properties of the cookies were determined, a more comprehensive assessment of these bakery products can be conducted to delve into their sensory attributes and nutritional quality.The different types of chickpea flour had their own characteristics, and one of the most significant differences was related to the water retention capacity of the flours. CCF had the highest water retention capacity and had a value that was approximately 119.7% higher than that of RCF. Due to the differences in their characteristics, the doughs and cookies made from these three types of flour also had differences in their properties. The cookies with GCF had the highest baking weight loss and spread ratio, while the RCF-containing cookies were the hardest. Considering the rheological properties of the cookie doughs, the most suitable dough for shaping was the one made with CCF. Our observations during the cookie preparation process also support this information. The cookie doughs made with GCF and RCF were stickier than the dough made with CCF; therefore, the cookies made with CCF had the best handling properties, with nice shape and visual properties. The RCF-containing cookies had the highest proportion of RS, followed by the cookies with GCF. Considering the sensory features, there were no statistically significant differences in the sensory parameters of the cookies. As with the different types of chickpea flour, the cookies made from these flours possessed distinct characteristics, making them suitable for the gluten-free market due to their favorable nutritional attributes. In addition, other types of legume flour, such as carob flour and/or nut flour, can be combined with these different forms of chickpea flour to improve the flavor properties of the cookies.


We show that non-monetary narratives highlighting prosocial or achievement motivations are 55% more effective in creating responses from businesses than narratives emphasizing monetary gains. These findings are robust across most narrative and audience characteristics, including age and language. Our findings suggest that communication towards business leaders around sustainability can be multi-pronged and should incorporate prosocial and achievement motivations aside from articulating potential financial benefits.The dominant narrative to motivate business actors to take climate actions emphasizes opportunities to increase monetary gains, linking sustainability to the financial goals of these organizations. The prevalence of monetary motivations in sustainability communication among businesses, consultancies, academics and international organizations has made this narrative a truism in the private sector. We conducted an online, real-world, large- Global efforts to address the climate crisis require businesses, alongside governments, individuals, non-profits and other organizations, to act decisively to dramatically reduce emissions  to respond to climate change messaging is important because they constitute the bedrock of economies worldwide. For example, they make up 99% of all businesses in the European Union and contribute 60–70% of industrial pollution, while in Canada the more than 1.2 million SMEs emit 200 tons of carbon annually, which is equal to the emissions of the country’s transportation sector  such as a drive to excel, love of a challenge or sense of duty. These forms of motivation are associated with entrepreneurial activity  might pursue climate action  to identify monetary, prosocial and achievement motivations in relation to why they realized climate action. The business owners are real individuals, each of whom has their own mix of reasons and motivations for engaging in climate action. Of the 13 business owner protagonists, seven were identified as male, six as female, two as visible minorities and two as Indigenous. These protagonists represented the agriculture, building, manufacturing and retail sectors, and seven of the ten provinces in Canada.www.gopivot.org. All material included for this research can be found online in the Open Science Framework repository (https://osf.io/suyq5/) including the three different narratives for each protagonist.In a second step, based on the in-depth interviews, we developed narratives for each protagonist. The data that we collected through the interviews on each protagonist typically integrated more than one motivation. Therefore, we worked with professional copy editors to create three separate texts for each protagonist, one each for monetary, prosocial and achievement motivations. Thus, in total, we developed 39 article-based narratives (13 stories for each motivation), averaging 795 words per story. These stories were made accessible at the time of the experiment on the project’s website We launched an experiment on Facebook to test the effectiveness of the three narrative motivations. Since it was not possible to portray the full version of the article-based narratives as part of the experimental setup on Facebook, we developed short summaries that conveyed the main motivation (we refer to these shorter versions as ‘narrative summary’ hereafter). Each narrative summary served as a “teaser” on Facebook, consisting of a concise description of one of the 39 narratives, averaging 76 words see Fig. . Each naThe experimental setup and the Facebook infrastructure enabled us to distribute each narrative summary to a predefined target population. Given that Facebook does not require its members to accurately identify their jobs or business affiliations, we leveraged interest-based targeting offered by the Facebook platform to best reach individuals who are SME owners. Specifically, we targeted individuals who indicated to Facebook an interest in one or more of the following categories: small and medium enterprises, shop local, sustainability, business development, human resources, social innovation, risk management, entrepreneurship. We further limited our sample population to people residing in Canada to correspond with the context of the protagonist featured in the narratives. According to Facebook, the potential reach of this sample population was 800–900 k members. With this targeting strategy, we attempted to find a balance between over- and undersampling SME owners. Undersampling might occur if targeted audience members are SME owners, but do not indicate interest in the “Small and medium enterprises” category on Facebook. By contrast, the selection of a large number of interest-based categories would have created the risk of introducing Facebook members into our sample who are not SME owners. Our targeting criteria, therefore, attempted to balance out these two undesirable/extreme scenarios. It is important to note that while Facebook uses interest topics for targeting, it does not share this information, barring us from identifying, post hoc, the interest-based keywords of Facebook members to whom the narrative types were shown.The experiment was conducted over ten days  on Facebook to randomly show the narrative summaries to the target audience. The narrative summaries were presented in a true-to-life social media environment as individuals looked through their own personal Facebook Newsfeed. We employed the Ads Manager tool provided through the Facebook Business Suite application to set up our sample and conduct our experiment . In each of these blocks, we placed 39 narrative summaries in English (13 protagonists* 3 narratives). We then replicated this experimental design and replaced the English narratives with the French translation to target English and French speakers separately. We used Facebook’s proprietary “Optimization for Ad Delivery” algorithm and selected the option of maximizing the target audience, in line with the outreach objectives of the action research collaboration. As a result, the 78 narratives (13 protagonists* 3 narrative types* 2 languages) may differ in terms of impressions . We have no reason to believe that this design choice created any systematic bias for/against any narrative type such that summaries of a given narrative were shown more/less frequently to individuals who were more likely to engage vis-a-vis another narrative. Moreover, in a post hoc Kolmogorov–Smirnov (K–S) test, we were able to confirm no biases in age between the samples that viewed the different narratives.Facebook recorded whether audience members clicked on the various parts of the ads. We used the number of clicks as a proxy for the number of people interested in the narratives. We employed two variables to measure engagement: clicks on the hyperlinks (hereafter ‘link clicks’) and clicks on other parts of the narrative summary (hereafter ‘narrative clicks’) . The estimation of the protagonists’ age was coded as “Protagonist age.”https://osf.io/suyq5/).To assess whether businesses were interested in the climate change narratives distributed through our experiment, we analyzed the effect of each narrative type and demographic characteristics—such as language and age—on audience engagement. Furthermore, we analyzed the perceived age and gender of the business owner protagonists that were featured in each narrative to assess their influence on audience engagement. For a detailed results report, see the online material in the Open Science Framework repository , we used a generalized linear mixed effects model. Exposure to a narrative summary is tracked by Facebook through impressions which refers to the number of individuals in the target audience in whose social media feeds the narratives appeared. The dependent variable for our analysis was either 0 (for no click) or 1 (for click) for each instance in which an audience member was exposed to one of the narrative summaries. To obtain this measure, we disaggregated the count data we received from Facebook into separate rows, with each row corresponding to an impression. We specified a logistic regression model with a random effects term to account for differences between individual protagonists. The mixed effects specification allowed us to consider each of the 13 protagonists as a distinct experiment in which we tested the effects of the three different motivations. Whether the Y is a vector of control variables pertaining to the protagonists, capturing protagonists’ age and gender. Z is a vector of control variables pertaining to the Facebook audience, capturing audience age and language as per the 10 Facebook blocks described above. E is an error term capturing all remaining variance. We ran our analysis using the lme4 package in R.Here, prot = 0,…,12 corresponds to each of the 13 protagonists. X is our main independent dummy variable indicating narrative types . As a robustness test, we modelled the effect of narrative type on our second dependent variable, namely narrative clicks (which excludes link clicks). This variable was collected in the same manner as the other data used for our main analysis. Because each member of the target audience could click more than once on a given narrative, we deemed a logit model inappropriate. We thus fit a generalized mixed effects linear model with a negative binomial link function to model this dependence, controlling for the same set of covariates as in the model described above. Instead of analyzing the odds ratio as done for the logistic regression model, we measured the incident rate ratio to examine multiple, non-mutually exclusive interactions within in one narrative. We chose a binomial distribution to account for overdispersion . Raw data and materials and the custom codes for analysis are available in the Open Science Framework repository.Collectively, the 39 narrative summaries, which were shown to 5 different age groups in English and French on Facebook, gained 94,712 impressions. In total, we recorded 540 clicks on hyperlinks (= “link clicks”) and 1773 clicks on other items (= “narrative clicks”) across the three narrative types.p = 0.015, 95% confidence interval (CI) = ].Results of our logit model are presented in Table p = 0.025, 95% CI = ] is statistically indistinguishable from responses to narratives that explained the climate actions of a business owner protagonist with achievement motivations .Considering that non-monetary narratives outperformed monetary ones, we analyzed more closely the difference between prosocial and achievement motivations in climate change communications. We find substantively similar effect sizes for narratives describing the protagonists’ motivation that highlighted, for example, their concern for the environment  and for narratives that emphasized their sense of duty . The likelihood of individuals clicking on narratives that describe prosocial motivations [OR = 1.51, We investigated effect sizes for several audience characteristics to discern whether the observed effects were generalizable within our sample. When analyzing the effect of the perceived protagonists’ age  on audience responses to the three narratives we found no influence Table . At the p < 0.001, 95% CI = ). However, in this case, we did find that the achievement narrative performed better than the prosocial narrative ; achievement narrative: IRR = 1.96, p < 0.001, CI = ).We performed similar analyses with narrative clicks instead of link clicks as the dependent variable ; prosocial narrative: OR = 1.94, p = 0.013, CI = , achievement narrative: ). We found the opposite effect when analyzing narrative clicks: achievement and prosocial narratives that featured male protagonists performed significantly better ; prosocial narratives: IRR = 2.26, p < 0.001, CI = ; achievement narratives: IRR = 3.74, p < 0.001, 95% CI = ).We did not obtain clear-cut results when we analyzed the effect of the protagonists’ gender on how audiences responded. When analyzing link clicks, we found audiences responded about twice as much to achievement or prosocial narratives featuring female protagonists  competitive advantage by increasing customer loyalty and willingness to pay, (ii) realizing greater efficiency, lowering costs or reducing risks in operations and supply chains, (iii) or spurring innovation and new product and service development (Reinhardt We found, contrary to what is typically assumed, that suasion through economic discourse is less effective even for business organizations. Employing prosocial and achievement motivations when communicating about climate actions is, based on our experiments, 55% more effective in generating interest than narratives that employ monetary motivation. Importantly, prosocial and achievement narratives both perform better than narratives expressing monetary motivations. These findings are robust across a variety of protagonist and audience characteristics, including age and language.Our study design advances research on the effectiveness of monetary versus non-monetary motivations by overcoming constrains undermining past studies. Related research has been predominately restricted to laboratory settings (e.g., Hafenbradl and Waeger A key contribution of our research to the literature on sustainability communication is in shedding light on the effectiveness of distinct narratives in real-world settings. While personal motivations play a crucial role in people’s sustainability commitment (Schaefer et al. Narratives are most likely to strike a responsive chord, if they are woven into tangible stories and align with the lived experiences of target audiences Hulme . For thiUltimately, this research reveals the most effective approach for sustainability communicators when approaching business audiences in the context of climate change. Importantly, our research focused exclusively on revealing what motivations are most effective in garnering initial interest in sustainability topics. Our research design did not assess where such communication leads to long-term commitment and implementation of climate actions. It would be valuable for future research to understand whether motivations that lead to initial engagement are also meaningful for generating lasting interest (Rode et al. homo economicus, driven only by financial considerations (Wegner and Pascual In terms of guidance for sustainability communications, our study yields three practical implications. First, climate change communication directed towards businesses should not be limited to emphasizing potential monetary benefits. To be clear, our findings do not suggest that monetary motivations or mention of monetary issues in communications about climate action should be discontinued. Such communication will be effective for some audiences, and for many others, are likely to be complementary to other rationales for pursuing climate action (Asensio and Delmas Second, our results provide support for narrative-based communication approaches to promote desirable actions, even for business audiences. In particular, climate change narratives could become more effective by explicitly foregrounding prosocial and achievement motivations to engage audiences with climate action and, more broadly, sustainability. By focusing on pluralistic framings, sustainability messaging can benefit from a multiplicity of stories, moving beyond a single dominant narrative to employ complementary rationales for pursuing climate action (Luederitz et al. Third, our research demonstrates the usefulness of articulating the challenges and successes of real people in advancing sustainability (De Meyer et al. In business settings, people are often assumed to act rationally with the sole aim of maximizing profits, thereby neglecting the multi-dimensional motivations at play when sustainability actions are undertaken. By testing different motivations encoded in non-overlapping narratives, we are able to show their relative leverage. Our findings advance previous studies that have assumed one-dimensional identities of audiences, associating a given actor with a single narrative. Instead, our research demonstrates the need for pluralistic understandings when dealing with the aspirations and motivations of societal actors. Employing complementary rationales, such as monetary, prosocial and achievement motivations, when engaging audiences in conversations about climate action would significantly advance the effectiveness of sustainability efforts. Future research should move beyond assumed narrative–actor associations, and examine the situational circumstances under which protagonists and audiences gravitate toward certain narratives.The findings of our study advance narrative research as we demonstrate the effective use of relatable, real-world protagonists for highlighting challenges, achievements and questions encountered when people attempt to realize climate actions. Often sustainability communication is centered around success stories to entice audiences to join concerted efforts against climate change. The reality is that attaining sustainability goals—as is the case for realizing any course of action—is a challenging undertaking with setbacks, triumphs and conflicts. Our research placed the unique experiences of people at the center of narrative development to create authentic human stories that highlight real events and actions. Future research can advance this approach by moving beyond fictional characters and success stories to develop effective actor-specific messaging. To advance our work, research is needed on the particularities under which story elements that focus on failure, success and struggle resonate with specific subsets of audiences.Our research has shown that efforts to encourage businesses to address climate change are likely to be more effective if multi-pronged and—alongside monetary justifications—the employed narratives emphasize prosocial and achievement motives. Considering the tremendous challenges in the transition to a low-carbon economy, our research offers a promising entry point for communication aimed at engaging people in ambitious climate actions.


A numerical model was developed to analyse the behaviour of the biomimetic structures under compression loading. Further, a damage examination was conducted through optical microscopy and profilometry. The results showed that the cornstalk-inspired biomimetic structure exhibited a superior specific energy absorption (SEA) capability that was three times higher than that of the other core designs as reported in the literature.This paper presents an investigation on the stiffness and energy absorption capabilities of three proposed biomimetic structures based on the internal architecture of a cornstalk. 3D printing was used to manufacture specimens using a tough and impact-resistant thermoplastic material, acrylonitrile butadiene styrene (ABS). The structural stiffness, maximum stress, densification strain, and energy absorption were extracted from the compression tests performed at a strain rate of 10 Porous structures exist in biological materials, such as the wall of a pomelo, a lotus root, a turtle shell carapace, and bone ,2,3,4. TMost plant stems are lightweight biological composite materials with superior stiffness-to-mass ratios compared to those of metallic materials such as steel and aluminium ,18,19. ICornstalks are thick and strong structures . They caThe stem of a plant and thin-walled engineering structures have many similarities: (a) both can be tubular structures or filled structures, (b) both absorb energy during deformation, and (c) both are subjected to static and dynamic loads. One of the key characteristics of agricultural crops is their loading resistance. It is also suggested that the combination of the light weight and high strength of the stem structure provides a natural advantage. Therefore, this can provide us with new ideas for the design of energy-absorbing structures.Cornstalks resemble a composite filling structure. The inner medullary core of its stem is a foam porous structure with a similar function to that of a foam core, significantly so when it can sustain its weight or other compressive forces . The croMany scholars have investigated the properties of cornstalks themselves. For example, He and Wang  analysedBased on the principle of engineering mechanics, biomimetic structures are inspired by studying the architecture of organisms at different structural length scales. Song et al.  mimickedDue to the porous architecture of biomimetic structures, their smart usage could greatly influence fuel consumption in the automotive industry due to higher fuel efficiency and a lower carbon footprint. In the case of electric vehicles, reducing the weight of the vehicle could potentially increase the driving range powered by batteries. Some examples include a diesel piston, a fluid pump, and a racing car cylinder head . In all This paper investigated a novel bioinspired cornstalk structure that was mimicked on the meso scale and that was subjected to compression. We present the energy absorption capability results and analysed some failure mechanisms identified through structural deformation. These objectives were achieved by employing a numerical model coupled with experimental approaches. The effect of the geometry of the biomimetic structure on its energy absorption capability was investigated. We also present an understanding of how the biomimetic-designed structures performed comparatively with other porous structures in a literature review. To mimic the tough and impact-resistant characteristics of a stem, acrylonitrile butadiene styrene (ABS)—an oil-based thermoplastic—was chosen for the three-dimensional (3D) printing of the specimens. The geometrical design and the computer-aided design (CAD) models were developed for the printing of the specimens.This study investigated the energy absorption capabilities of a cornstalk on a meso scale with respect to its building blocks and was designed by replicating the vascular bundles and medullary core, which can be seen under a microscope. It was not aimed to study the entire hierarchical structure of the stem, as replicating all the stem’s structural features and mechanics may require several techniques at different length scales. Simplified models of a stem-like structure were designed representing reinforcement with cylinders embedded in a porous matrix. The authors paid attention to keeping the designed structures at a constant volume ratio near 60%, which is similar to that of the structures found in plants . The biomimetic approach dictates that, when mimicking nature to create engineering designs, it is essential to keep the relative density of the designed structures (that is mimicked) close to the relative density of the natural mimicked source to have a fair comparison. As a result, we kept all of our samples close to a 0.6 relative density to claim the structures as “biomimetic”. We investigated the effect that the geometry of the biomimetic-designed samples had on their energy absorption capabilities by varying the thickness of the tube reinforcements and the spacing between the outer surfaces of the adjacent tubes. We intended to understand whether any geometric variations (while making sure that the relative density was close to 0.6) would affect the stiffness of the biomimetic structure. Hence, we did not introduce many variables with different relative densities (not the same as in nature), as this would divert the relative density away from the natural source of inspiration. The dimensions of the designed samples were based on ASTM C393 and are stated below in wt) of the tubes (1.5 mm) and (ii) the spacing (s) between the outer surfaces of the two adjacent tubes (3 mm). Taking specimen T1.5S3 as an example, the naming of the samples was mainly composed of two parts: (i) the thickness  was used to fabricate the specimens. ABS filaments, supplied by UltimakerTM, were chosen as the printing material in this study. ABS filaments can produce high-quality prints based on their roundness and consistent diameter. The manufacturer specifies these filaments to minimise warping and to ensure consistent interlayer adhesion. They are also tough and impact resistant, which are desirable characteristics for characterising energy absorption. It was reported that the maximum compressive force experienced by a cornstalk was 140 N at a displacement of 6 mm under compressive loading [The convenience of printing smaller parts with minimal defects or warping effects;Its ability to identify all the properties needed for numerical modelling;The yield strength (An in-house fused deposition modelling (FDM)-based 3D printer, Ultimaker loading . As a re2.5 MPa) . This ma® Universal Testing Machine  with a 100 kN load cell was employed in the experiment. Three samples were tested at a fixed loading rate of 1 mm/min. To determine the mechanical properties of the base material used to fabricate the biomimetic structures, the tensile properties of the printed samples were characterised. Tensile test samples were designed according to ASTM standard D638 . A summaThe 3D printer was carefully calibrated to obtain the best quality printed specimens. Calibration is imperative to achieve an excellent final product. It programs the printer to extrude the right amount of ABS and allows for the precise rotation control of the print head. As for the printing parameters, optimised settings were taken into consideration from Gorana et al. . The pri® Universal Testing Machine (AG-X) with a load capacity of 100 kN. Testing was performed using displacement control mode at a loading speed of 1.38 mm/min, which resulted in a strain rate of 0.001 s−1. All printed specimens were kept at room temperature inside a sealed bag for optimum storage conditions as suggested by the filaments supplier for at least 24 h before mechanical testing commenced. The loading curves were observed to determine the energy absorption during the compression process until 60% strain (densification region) of the full height of the specimen was reached.Quasistatic compression tests were conducted on the printed biomimetic porous sandwich specimens along the uniaxial direction  to investigate their compressive loading behaviour and energy absorption capability. The tests were conducted using ShimadzuIt is essential to analyse the structural deformation where the material has plastically deformed for energy absorption applications. The postmortem damage analysis of each specimen was conducted in three steps on two sections of the specimen as illustrated in Cutting and grinding: The Buehler IsoMet Low Speed cutting machine was utilised to section the specimens precisely. Upon completing the cutting process, Tegramin from Struers was used to grind the sectioned specimens finely.Stereo microscopy: ZEISS SV8 stereo microscope was used to identify the defects and failures in the specimens during the compression process. A Canon SLR was used to inspect the damages in the specimens and to capture images.Optical profilometry: A full 3D scan of the damaged specimens was taken using NANOVEA Optical Profiler. The purpose of the profilometry was to profile surface morphology to perform a quantifiable analysis and to understand the surface roughness after cutting the sample using a diamond blade.The three steps were:A numerical model was developed using finite element explicit code LS-DYNA  to provide detailed information on the quasistatic response of the biomimetic structures. Some of the information collected was predictions of failure mechanisms, energy absorption capabilities, the evolution of the stress field, and validation of the experimental results. The model was built using the experimental setup. Only a quarter of the biomimetic porous sandwich structure, compression platen, and bottom support was created to improve the computational efficiency because of the symmetry of the setup as shown in Since the sandwich structure incorporating various shapes and geometries would undergo deformation during the compression process, a small mesh size of 0.25 mm discretised the part. The adopted mesh size was verified to be adequate for producing converged results by a mesh sensitivity analysis. Solid elements were used to model the biomimetic structural part. The part was meshed using tetrahedral solid elements with 1 point tetrahedron (ELFORM = 10) to overcome negative volumes in large deformation and distortion situations. The degree of freedom (DOF) of the bottom support was all constrained to simulate the fixed boundary condition, and the symmetry boundary conditions were imposed on the symmetry of the sandwich structures. Using the example of the X-Y symmetry plane from , the symTranslational constraint in the local z-axis for degree for freedom (DOF)Rotational constraint in local x-axis for degree of freedom (DOF)Rotational constraint in local y-axis for degree of freedom (DOF)Boundary set conditions:The compression platen was only allowed to translate in the y-axis by restricting the DOFs of its nodes, except the y-translation node, and the initial velocities following those in the compression tests were applied to the compression platen. The contact between the plates and the sandwich structure was modelled with the automatic surface-to-surface algorithm. In addition, the interior contact treatment was applied using automatic self-contact to the solid elements of the core to keep them from merging or inverting. For high-strain modelling, automatic surface-to-surface conditions are a recommended contact type (according to LS-DYNA theory guidelines), as the orientation of parts relative to each other cannot always be anticipated because the model undergoes large deformation. The chosen contact treatment also checks for penetration on either side of the elements. During the experiment, dry surface conditions were used, and no visible slippage was observed. As such, the static coefficient of friction was applied in the contact treatment.3, Young’s modulus of 210 GPa, and Poisson’s ratio of 0.3. The core was modelled with simplified Material Type 03 (*MAT_PLASTIC_KINEMATIC), which ignored the thermal effect and damage, with the ABS material properties listed in In the experiment, the deformation of the steel crosshead (100 kN) after tests was negligible. In the numerical simulation, therefore, the compression platen was assumed to be rigid and was modelled with Material Type 20 (*MAT_RIGID) with a density of 7.85 g/cmThe data collected from the experimentation of the three different specimens with similar relative densities were processed to generate the stress (y) at a given strain increased linearly with an increase in the thickness of the tube in the matrix. Specimen T2.5S1 exhibited maximum yield stress, which was 13.3% greater than T2S2 and 29.1% greater than T1.5S1. On the other hand, Specimen T2.5S1 showed the highest stiffness compared to the other two specimens as shown in The key parameters governing the elastic behaviour of any material are yield stress and elastic stiffness. A few interesting characteristics of quasistatic compressive behaviour can be observed in The experimental curves were obtained from a set of repetitive tests conducted as per ASTM standard C365. Error bars are presented in the table for the standard deviation of the results obtained. The errors obtained can be attributed to measurement uncertainty, instrument error, human error, and a compliance test. The results are presented as nominal values. We did not consider logarithmic strain in our study due to its limitations on strain measurements in large deformation mechanics. The structural analysis performed on the printed samples in this article did not consider the variation of the cross-section area of the elements or the buckling phenomenon. Hence, it is considered a research limitation. d) of 0.47 ± 0.006. In contrast, specimen T2.5S1 had a densification strain (d) of 0.52 ± 0.006 as summarised in d) is the strain where the cells crush together and where the condensed material begins to strain. As the spacing between the tubes decreased, the samples could accommodate a higher portion of the tubes at the edges in a given volumetric fraction. This explains the underlying mechanism of the enhanced force resistance, stiffness, and larger plateau region of biomimetic specimen T2.5S1. Therefore, these structures exhibited more prolonged plateau stress after the onset of plastic deformation and large densification strain. On the contrary, specimens T2S2 and T1.5S3 had thinner tube walls and a higher number of pores in their volumetric fraction. More cell walls could deform and occupy the void spaces more systematically, enabling deformation to considerable strains yet not enabling strains larger than that of specimen T2.5S1.For a given shape, the geometry and relative density of the biomimetic structures significantly affected the plateau slope. Specimen T2.5S1 was observed to have the largest plateau region compared to T2S2 and T1.5S3, as both of these specimens experienced an early densification strain (m) (74.3 ± 0.3 MPa) during the compression test at a 60% displacement limit. In comparison, specimen T2S2 exhibited a 7.8% lower maximum stress, and T1.5S3 exhibited a maximum stress that was 15.6% less than that of T2.5S1. The sandwich structure was nearly densified to a solid when the displacement reached 14 mm . In other words, the structural hierarchy was no longer effective beyond this point, implying that the specimen would nearly become a solid piece and that all the specimens were expected to behave similarly. Usually, the mechanical response of energy-absorbing structures maintains a reasonable constant stress over an extensive plastic strain regime. Therefore, the structures absorb large amounts of energy before reaching full densification to avoid excess stress transmission. Specimen T2.5S1, which had the thickest tube wall and the smallest spacing distance between the tubes, exhibited maximum stress . It is a well-known fact that the porosity and stiffness of lightweight structures are interrelated. Similar findings were observed in our biomimetic structures. Tube thickness and spacing were tuned to identify which sample would generate a higher stiffness. A clear trend was seen in As the biomimetic specimens were demonstrated to have a larger plateau region with a near-constant load, they are more suited for crashworthiness applications, such as crash protection in vehicles, as a high energy absorption capability is the desired property for crashworthiness applications. However, one purpose of designing biomimetic structures is to serve lightweight applications. High stiffness and high specific energy absorption (SEA) are the prime desired properties for lightweight structural applications. Though specimen T2.5S1 was demonstrated to be stiffer among the three, based on the above findings, it is still unclear which specimen design is more suitable for lightweight applications as mass was not considered during the analysis. As a result, this is further discussed in d) and where In addition to the yield and plateau stress, the metric of greatest interest for comparative purposes was the specific energy absorption (SEA) for the proposed biomimetic structures inspired by the internal structure of a cornstalk, which is a measure of the amount of energy absorbed per unit mass (unit: kJ/kg) and which is expressed mathematically by Equation (2):This measure could be arrived at by dividing the area under the force–displacement curve by the measured mass of the biomimetic structure under compression. It denotes the energy dissipated by the specimens due to the intermolecular dislocation in the strain-hardening process. The amount of SEA was calculated for each specimen design loaded up to 60% strain as summarised in It was identified that the biomimetic design specimen T2.5S1 outperformed the other specimen designs of the same sample size when compressed to 60% of the initial height. Specimen T1.5S3 could absorb 29.7 ± 0.05 kJ/kg during the overall compression stage until the densification region. The absorption capability increased by 7.4% (T2S2) as the thickness of the tube increased by 33.3% (2 mm), and the spacing between the tubes decreased by 33.3% (2 mm). Consecutively, the absorption capability further increased by 13.5% (T2.5S1) as the thickness increased by 66.6% (2.5 mm) from the original, and the spacing between the tubes decreased by 66.6% (1 mm). The data findings denoted that, as the mechanical properties of the specimens were tuned through relative density variation and architectural modifications, it significantly impacted the SEA characteristics of the biomimetic structures. It is equally important to point out that the mass of specimen T2.5S1 (15.7 ± 0.06 g) was 5.73% higher than specimen T2S2 (14.8 ± 0.06 g) of the same sample size, and it was 8.28% higher than specimen T1.5S3 (14.4 ± 0.06 g) of the same sample size. This suggests that weight should not be the only parameter taken into consideration for making improvements, as constantly lowering the weight can jeopardise the structural strength of the samples themselves. As a result, the relative density of the designed samples is an essential aspect to consider when designing. It should be noted that designing thinner tube walls significantly reduces weight and decreases the energy-absorbing capability as seen in the case of specimen T1.5S3. It was postulated that the stiffness and the amount of the energy absorption of the biomimetic structures (at a 60% relative density) would continue to increase when the mechanical properties were tuned through geometrical modification. However, further tuning the mechanical properties will gradually change the relative density of the biomimetic structure. As such, further investigation will be needed to understand how varying the geometry of each element of the specimen contributes to the stiffness and absorption capability at different relative densities, even though the relative density of the manufactured specimen would deviate away from the relative density of the cornstalk itself. Lastly, The biomimetic structures showed significant localised stress from the beginning of the compression. Deformation initiated at the comparatively weaker cell walls of the pores located in the middle (perpendicular to the compression axis) of the specimens along the walls of the inner tube with increasing strain as shown in As the top edges of the pores moved towards the bottom edges, the pores subsequently changed their shape from circular to elliptical geometry as shown in An examination of the failed tubes at the plateau regime indicated that the crushing process led to the middle region of the inner cylinder splaying outwards as shown As the barrelling phenomenon continued, the localised strain was observed in the middle of the inner tube as the expansion propagated laterally as illustrated in A quick observation of the surface morphology in On the other hand, it was interesting to see in Lastly, the facesheets were observed to expand plastically during the compression process until 60% strain was reached, and the compression test was stopped. As more significant efforts were required to collapse the pores, deform the tubes, and expand the facesheets, a rapid increase in steepness was demonstrated by the rapid increase in the stress experienced in the densification region. For specimen T2.5S1, it was observed that, as the bottom facesheet expanded plastically, it started failing at the centre of all four edges as shown in The finite element simulations of the compression tests were conducted using 3D CAD geometry to manufacture the experimental specimens to validate the numerical simulation using the same experimental conditions. The numerical simulation could extract the contact force between the compression platen and the sandwich structure. The displacement data are available from the translation movement of the rigid compression platen. Therefore, the simulation results were compared with the experimental data in terms of the stress–strain response, energy absorption capability, and structural collapse mechanisms to show the reproducibility of the modelling approach.s), as it was slightly lower than the experimental data. With increasing strain, local deformation occurred in the pores and tube walls, leading to a drop in the max stress (m) in the experimental data. The simulation results systematically overestimated the maximum experimental stress (m), which is a common occurrence as stated in previously studied additively manufactured samples [ samples ,57,58. AThe simulations of the compression test were run with a perfectly plastic assumption. In reality, localised defects are inevitable due to the 3D printing process. Warping and irregular surface features were some of the printed parts’ defects.The structure was assumed to be isotropic, i.e., a uniform base material property throughout the structure. However, this analytical model did not consider material anisotropy due to the 3D printing process.The structure was assumed to have a uniform relative density during modelling. However, the manufactured samples might not have had a uniform relative density due to microporosity in the printed layers.Given that the geometry of the designed specimens was symmetric and that force distribution was even, the quarter-symmetrical model was adopted to run the simulation reasonably, assuming the behaviour would be the same as the full model.The deformation of the tetrahedral solid elements underwent large distortion when the strain approached 30% and above. Two types of contact parameters were used to overcome the negative volume, and one point tetrahedron (ELFORM 10) was chosen. It was assumed that all of the elements in the sample would not have any negative volume, which could affect the numerical results.The compression plate was assumed to be rigid, and the material model was chosen accordingly.Some of the assumptions taken into account when modelling were as follows:The discrepancy between the experimental and numerical modelling results, as shown in m) encountered by the core was 18.5 ± 0.3 MPa as shown in m) of 22.7 ± 0.3 MPa, while the maximum stress (m) of the horizontal cell walls was much lower. That is, deformation initiated in the vertical cell walls due to compressive stress, whereas the horizontal walls experienced minor tensile stress and remained within the elastic limit. At the beginning of compression, an elevated-stress region was experienced by the core itself (green V.M contour) as demonstrated in Additionally, the top and bottom regions of the core at m) (22.2 ± 0.3 MPa) on the tube walls and vertical walls of the pores was significantly lower than the yield stress (y) (37 MPa) of the base material. In addition, there was no high-stress region observed in the facesheets of the sandwich structure.As the buckling phenomenon progressed to m) of 33.9 ± 0.3 MPa was concentrated at the centre of the structure, resulting in the propagation of the splaying process of the inner tube laterally. In contrast, the outer tube formed a C-shaped wall undergoing plastic deformation after the initial yielding of the structure. The independency of the top and bottom regions was first discovered once the samples were sectioned at different strains, and the deformation patterns were identified as shown in y) of the base material as a maximum stress (m) of 62.7 ± 0.3 MPa was achieved as shown in Lastly, it was observed in To predict the failure/deformation behaviour of the tubes and pores embedded in the biomimetic structure as modelling ran with a perfectly plastic assumption. The deformation pattern identified during the experiment could be different from that identified during numerical modelling due to defects in the samples or any possible human errors while conducting the experiments. In the end, it was noted that the deformation pattern observed during the experiments was acceptable as it was well matched with that observed during modelling.To understand the underlying hypothesis of the deformation behaviour through stress field distribution. This adds quantitative physical data on the deformation mechanisms which authors cannot collect solely from the experiment during the deformation process.To obtain the stress threshold for buckling, which can be determined through simulations to provide quantitative limits on the strain range for the given structure. In our study, the stress threshold for buckling was determined to be 21.3 MPa–42.5 MPa on a strain regime between Overall, the purpose of numerical modelling was as follows:To obtain stress contours that could be used to design better geometries for specific applications. In numerical modelling, variations can be made at relatively low costs and can be simulated rather than being made through the expense of 3D printing and being made by conducting experiments.To perform data validation on the stress–strain responses of the experimental and modelling results. Visualising the trendline  than the other designs. It was noted that, as the thickness of the tube increased by 33.3%, the stiffness of the biomimetic structure increased by 23%.Regarding SEA, the biomimetic-designed specimen outperformed the other types of cores, such as foams, honeycombs, lattices, and truss cores. This suggests that the proposed designs offer the potential for use in designing lightweight energy-absorbing structures.The outer tubes failed due to the delamination of the layers in the tube walls, buckling, and crack initiation, leading to the separation of the foam core from the tube walls embedded within the matrix. Such a failure suggests that a significant amount of energy was absorbed during the compression process. The inner tube walls splayed outwards in the lateral direction during the crushing process. Localised stress was observed at the centre (perpendicular to the compressive axis) of the inner tube as the expansion propagated.The geometry of the pores changed and deformed plastically during the crushing process. It was noted that the vertical cell walls were more responsible for enhancing the plastic response during compression.The developed finite element model produced accurate and reliable results regarding the biomimetic structures’ stress–strain response, energy absorption, and deformation pattern with less than a 6% error. The difference in the results was not significantly large.The naming of the samples  was mainly composed of two parts: (i) the thickness of the tubes (1.5 mm) and (ii) the spacing between the outer surfaces of the adjacent tubes (3 mm). Based on the results, the main conclusions were as follows:As well as identifying how the structure deformed and failed during the compression process, this study has shown the potential for superior performance in energy-absorbing applications of cornstalk-inspired lightweight porous structures.


Graph convolutional networks (GCNs) have achieved impressive results in many medical scenarios involving graph node classification tasks. However, there are difficulties in transfer learning for graph representation learning and graph network models. Most GNNs work only in a single domain and cannot transfer the learned knowledge to other domains. Coronary Heart Disease (CHD) is a high-mortality disease, and there are non-public and significant differences in CHD datasets for current research, which makes it difficult to perform unified transfer learning. Therefore, in this paper, we propose a novel adversarial domain-adaptive multichannel graph convolutional network (DAMGCN) that can perform graph transfer learning on cross-domain tasks to achieve cross-domain medical knowledge transfer on different CHD datasets. First, we use a two-channel GCN model for feature aggregation using local consistency and global consistency. Then, a uniform node representation is generated for different graphs using an attention mechanism. Finally, we provide a domain adversarial module to decrease the discrepancies between the source and target domain classifiers and optimize the three loss functions in order to accomplish source and target domain knowledge transfer. The experimental findings demonstrate that our model performs best on three CHD datasets, and its performance is greatly enhanced by graph transfer learning. The root cause of coronary heart disease is the persistent buildup of fat or unhealthy cholesterol inside the artery wall, which eventually causes the artery wall to narrow and block2. Arrhythmia, myocardial infarction, and angina pectoris symptoms are the most common clinical signs of coronary heart disease. The main methods currently used in clinical practice for the detection of coronary artery disease include3: electrocardiogram (ECG), ECG stress test, echocardiography, ambulatory ECG, hematology, CT angiography, and other techniques. Among these examination methods, the diagnosis is usually made by a cardiologist by examining the ECG waveform, relying on the expert's long-term experience and subjective judgment. But these decisions can be supported and replaced to some extent by automated data-driven methods.Coronary heart disease (CHD) is a serious cardiovascular disease (CVD)4. End-to-end learning systems involving risk assessment prediction for diseases have four main steps, such as feature extraction, segmentation, normalization, and smoothing. Convolutional neural networks (CNNs) provide the best solution for classification in many fields, such as computer vision (CV), medical imaging, and natural language processing (NLP)5. Graph embedding algorithms mainly focus on the neighborhood of nodes and edges to extract knowledge, such as Netpro2vec6. However, deep learning approaches for healthcare have some limitations when training models using specific data, as the model requires large amounts of annotated medical data . The availability of large amounts of annotated data is complicated by privacy and cost issues.Deep learning (DL) techniques overcome the limitations of medical computer-aided diagnosis (CAD) systems to automatically extract discriminative features on image data7. Therefore, medical systems have to continuously collect immediate data like ECG. For deep learning, such datasets are always changing, the cost of training is increasing, and the difficulty of migration is also prominent. And transfer learning can handle these needs effectively.Healthcare systems produce enormous volumes of raw data every day in the big data age. Manual labeling is costly, data is easily outdated, and access to labeled data is difficult. In this instance, it's possible that the labeled data acquired during one time period won't have a similar distribution throughout the subsequent time period. For cardiovascular data, data from patient clinical visits reflects postoperative recovery, while abnormal data often arises from rhythm variability at future moments9 seeks to take information from one or more source tasks and apply it to the target task. Xu et al.10 proposed a deep-transfer CNN framework for EEG classification. It transfers the pre-trained VGG-16 CNN model to the target CNN model for EEG classification, and improves its classification accuracy through fine-tuning of post-layer parameters. However, the transfer ability of the pre-trained CNN model on different layers has not been investigated. Tadesse et al.11 proposed an end-to-end trainable cross-domain transfer learning CVD diagnostic model that analyzes the fusion of multiple ECG leads in combination with spectrogram stacking alignment. However, the high-dimensional processing of CNN features was neglected. Lakshmi et al.12 used CNN architecture and transfer learning techniques to measure carotid intima-media thickness (CIMT) from ultrasound images of type II diabetic subjects in combination with the Framingham Risk Score (FRS) to achieve a good prediction of CVD risk. However, it is difficult to transfer to other cardiovascular datasets.Recently, transfer learning (TL) has been used in the fields of medical imaging, medical healthcare, etc. Transfer learning13. Therefore, TL cannot be directly applied to problems such as node classification, link prediction, and graph classification in graph neural networks (GNN)18. It is due to the phenomenon of graph isomorphism that such network-structured data with nodes and links with different relational edges requires rotation invariant models. When models need to be transmitted across networks to handle the same task, they may suffer from embedding space drift19 and differences in embedding distributions20. Existing methods rarely model the GNN cross-domain network structure information, which is central to node classification.However, research on transfer learning has mainly focused on the fields of CV and NLP. Images in CV and sequence samples in NLP are independently distributed, and they rarely require rotation invariance of the model. Unlike CNN, such network-structured data with nodes and edges requires model rotation invariance. For example, in biochemistry, isomorphic graphs of drug molecules exhibit different effectsWe study the graph transfer learning problem on the CHD dataset for the first time , where the already labeled source network is used to assist the target network for node classification by means of graph convolution and adversarial domain adaptation.In the node feature extraction layer, we use the local and global consistency relations of each graph to assist the training of the node embedding module. And the attention mechanism is used to unite the local and global relations for a comprehensive node representation of each domain.We consider source domain information, adversarial domain information and target domain information simultaneously, and learn domain invariant and semantic representations to reduce domain differences across domains. Cross-domain experiments on three real CHD datasets show that DAMGCN outperforms state-of-the-art single-domain graph representation learning models.In summary, the following challenging problems are still faced in CHD risk classification applications: (1) Deep learning models often need to be trained on a lot of labeled data. However, most CHD datasets are unlabeled or missing, and experts cannot manually label all samples. (2) Training deep learning models from scratch is very time-consuming and computationally intensive. (3) There may be significant differences between source and target data across domains, with few common attributes. To address these three challenges, in this paper, we propose a supervised adversarial domain-adapted multichannel graph convolutional network (DAMGCN) for cross-domain node classification. It models the local and global consistency relationships of each graph and combines source information, adversarial domain, and target information into a unified deep model. The main contributions and innovations of the article are as follows:21.The cardiovascular medicine division of a tertiary care hospital in the Fujian Province of China contributed some of the genuine hospital patient data that was used in this investigation. The dataset includes data from CHD patients collected through return visits during the five-year period from 2016 to 2021. It includes 5850 patients who had procedures (coronary angiography and PCI for revascularization) discharged from the hospital, with 430 records for each index per patient, totaling approximately 2515,500 records. The original dataset contains a large number of missing patient records, as well as problems such as noise and irregularities. We did data preprocessing, including data cleaning, data conversion, missing value filling, and redundant data removal operations. Finally, the dataset was divided into seven major categories: basic patient information; past medical history; ECG indexes; cardiac ultrasound indexes; phlebotomy indexes; medication consumption; and coronary vascular lesionsThis research was approved by the Institutional Review Board (IRB) of Fujian Medical University Union Hospital . Interviews were performed after confirmation of informed consent. confirming that informed consent has been obtained from all subjects and their legal guardians. This consent process was approved by the ethics committee. All experiments were performed in accordance with relevant guidelines and regulations. H.Z.L. had access to information that could identify individual participants during or after data collection.22. The details of the experimental datasets are shown in Table We re-extracted two datasets related to all-cause mortality from the original dataset. We constructed graphs for both datasets based on the KNN approach: DNN is a multilayer perceptron (MLP) that uses only node features.DNN16 is a great deep convolutional network for graph-structured data that incorporates network topology and node attributes into a comprehensive learning framework. By default, we use KNN as the composition strategy (denoted as k-GCN).GCN: GCN18 as the main approach.p-GCN: A type of GCN, the graph structure used by the model is in the form of a population graph18 is characterized by having adaptive dual-channel graph convolution layers and attention layers represented as aggregated nodes to accommodate node classification for different tasks.AM-GCN: The optimal single-domain graph convolution model studied in DAMGCN: The model proposed in this paper. It is capable of performing graph convolution models for cross-domain node classification.To make a fair comparison with the model proposed in this paper, we use the following four methods as a baseline. Specifically, we compare this paper's approach with an advanced single-domain node classification model to verify the superiority of the cross-domain model. Later, the necessary comparisons are made between the variants of the model in this paper to analyze the role of each component.The experimental language uses Python 3.8.11, Scikit-learn 0.24.2, and the environment is the Pytorch 1.6.0 framework. Table 23. The dataset is imbalanced, and we also use MCC and balanced accuracy metrics to reflect its performance24. True positive (TP) and true negative (TN) values indicated correctly classified malignant and benign cases, respectively. False-positive (FP) and false-negative (FN) values indicate incorrectly classified benign and malignant cases, respectively. In our experiments, we used the macro-averaging technique to calculate the Precision, Recall, and F score of the model.In this work, we performed the task related to dichotomous classification on three CHD datasets. The results of the experiment were evaluated specifically using Accuracy, Precision, Recall, F score, and AUC (area under the ROC curve)18. Their respective advantages and limitations are summarized in Table We applied the advanced single domain model on 3 CHD datasets with the results shown in Table By comparing the cross-domain node classification, we observed an improvement in the predictive performance of different domains for All-cause death. In particular, although single domains can distinguish between true-negative and true-positive patient cases to some extent, there is an unbalanced distribution of sample proportions and an underdetection of death classes, which can be reflected in MCC (63.5%) and balanced accuracy (73.4%) performance. And after adversarial domain transfer, this problem can be improved. The best AUC performance of the model was achieved for the transfer of Heart level (H) to All-cause death (D). The AUC was improved by 4.7%, Recall by 4.9%, and F1 score by 4.7%. Thus, groups with a high Heart level contribute to the screening of All-cause death groups. For Mace occurrence (M) transferred to All-cause death(D), the best positive case prediction for All-cause death was achieved. The AUC was boosted by 3.7%, Recall by 6.8%, and F1 score by 5.3%. Thus, Mace occurrence and All-cause death data were similarly distributed and highly correlated, and both were highly transferable.Table The results show that by jointly modeling the consistency relationships of each graph, domain information, source domain information, and target domain information into a unified learning framework, the proposed DAMGCN can better capture the underlying representation of graph nodes and reduce the distribution gap across domains.Table DAMGCN¬t. To demonstrate the effectiveness of cross-domain transfer learning, we designed a variant model, DAMGCN¬t, to simulate the case of direct parameter migration. The only difference between DAMGCN¬t and DAMGCN is that DAMGCN¬t removes the target classifier loss from the model, i.e., it does not use information from the target domain, which is the core of cross-domain learning . The results in Table DAMGCN¬g. It belongs to a variant of DAMGCN that removes the global GCN layer of DAMGNN and uses only the local GCN layer. The effectiveness of the global GCN approach is investigated by comparing the two. The key between them is the presence or absence of using the PMI matrix. From the results, we found that the DAMGCN model outperformed DAMGCN¬g, with an improvement of 0.83% (H- > D) and 0.55% (M- > D) for all-cause death migration. Similarly, there was some degree of accuracy improvement for both the cross-domain tasks at the heart level and Mace occurrence. This confirms that the ability to extract node information using only the local GCN layer is limited, while the addition of the global GCN layer module containing the PMI matrix enables us to uncover potential relational nodes. And it combines local and global relations to capture a comprehensive representation of nodes.DAMGCN¬d. To verify the effectiveness of domain adversarial loss, we compared the DAMGCN model with DAMGCN¬d. DAMGCN¬d removes the gradient inverse layer of DAMGCN, i.e., the domain classifier. Without using domain adversarial loss, the source and target domains each train their own models and share some parameters, and this knowledge transfer is weak. Figure Since the proposed DAMGCN contains several key components, we compare variants of DAMGCN in this section to demonstrate the superiority of DAMGCN in terms of (1) the effect of target classifier loss; (2) the effect of the global GCN layer module; and (3) the effect of domain adversarial loss. The details are described as follows.25 method to map the learned embedding vectors into a two-dimensional space before the original features and the last layer of the depth model for each task, respectively. The presentation results of the datasets in Figs. To demonstrate the effectiveness of our proposed model more visually, we performed the visualization task on three CHD datasets. We used the t-SNE26. Our model consists mainly of three parts: (1) a dual-graph convolutional network module; (2) an attention mechanism module; and (3) a domain adaptation module. The DAMGCN model is shown in Fig. All the methods under this study were performed in accordance with the relevant guidelines and regulations of Fuzhou University (Fzu). The experimental protocols were approved by the Institutional Review Board (IRB) of Fujian Medical University Union Hospital. Informed consent was taken from all participants. In this section, we present our domain-adaptive graph convolutional network for cross-domain node classification. It is improved by the unsupervised domain adaptive network model proposed by WuGiven a source domain 9 is defined as follows: the domain can be represented as The important mathematical notation in deep transfer learning29. Domain adaptation can mitigate the detrimental effects of domain drift that occurs when knowledge is migrated from a source to a target by facilitating migration with models in different but related domains that share the same label space31. Several studies have also attempted to apply domain adaptation ideas to graph-structured data. The CDNE32 algorithm learns transferable node embeddings for cross-network learning tasks by minimizing the maximum mean difference (MMD) loss. But its modeling capability is limited. The AdaGCN algorithm33 uses graph convolutional networks as feature extractors to learn node representations and uses adversarial learning strategies to learn domain-invariant node representations. But it ignores the semantic information contained in the target domain samples. The UDA-GCN algorithm26 works similarly to ours, using a composite framework in order to achieve knowledge adaption between graphs. But it studies the problem of graph domain adaptation in unsupervised scenarios.Domain adaptation is a sub-theme of transfer learning that aims to migrate from a source domain with sufficient labeling information to a target domain with a large amount of unlabeled or little labeled data by minimizing domain differences34. The PMI metric performs well in semantic similarity tasks.Mutual information measures the amount of information contained in a given random variable about another random variable. It involves the reduction of uncertainty in one random variable due to the presence of another random variable. Assuming that the two random variables are independent, point-by-point mutual information (PMI) measures the difference between the co-occurrence probability of the marginal distribution given X and Y and the co-occurrence probability given their joint distribution35. The random walk utilizes the entire graph information to calculate the neighbor probability of each node. The semantic similarity between different nodes can be calculated by the random walk method. Then, using the semantic knowledge from frequency to frequency-based matrix, we finally get the PMI matrix.Frequency matrix: A random wander is a Markov chain that describes the order of all nodes visited throughout the wander. If the random wanderer is on node P matrix: From the frequency matrix (denoted F) obtained from Eq. , we first use the random walk-based method to calculate the frequency matrix. Random wandering has been used as a similarity metric in semi-supervised graph representation learning and graph classification problemsAccording to Eqs.  to 5), , 5), the36, it demonstrates that the graph's global information is more important. Our model trains two GNN modalities to extract features, thereby capturing both local and global information about the graph network. And we encode the semantic information of each node in the network separately. The node representation learning process consists of a local GNN and a global GNN. The local consistency implementation of the graph is to directly use the initial adjacency matrix to perform the graph convolution16 operation. This adjacency matrix can be the default or otherwise constructed as a single graph. The implementation method of the global consistency of the graph is the graph convolution operation based on random walk processing introduced in the previous section. This is shown below.16. We briefly describe InFor each domain, since the embeddings from the local and global consistency networks differ, i.e., contribute differently to the representation of graph learning, we use the graph attention module to obtain the importance of each domain's output. After performing graph convolution to extract features for the source and target domains, we obtain 4 embeddings from the local or global source graph embeddings We use the raw inputs We propose a model made up of a source classifier, a domain adversarial module, and a target classifier that jointly learn class discrimination and domain invariant node representation to improve the classification of nodes in the target network. This model aims to improve knowledge acquisition across domains and knowledge transfer to help with the task of node classification across domains. The model's loss function is constructed as follows:Loss of the source classifier. The source classifier loss d by Eq. .13\documLoss of the adversarial domain. The goal of the domain adversarial loss mize Eq.  during t40, which possess good learning and scalability. In our article, we implement adversarial training using the gradient reversal layer (GRL)27. GRL is defined in Eqs.  in Eqs.  and 15)40, whichIn this paper, we study the problem of cross-domain GNN transfer learning in healthcare. Most existing GNN learn models only in a single graph and do not consider knowledge transfer across graphs. Therefore, we propose a novel adversarial domain-adapted multichannel graph convolutional network (DAMGCN) to enable knowledge transfer between different CHD datasets. By using a dual graph convolutional network to aggregate the local and global relationships of graphs, we are able to learn better node representations in both source and target graphs. And the attention mechanism is combined to further generate uniform embeddings for downstream node classification tasks. By using cross-entropy loss in source domain classification, domain adversarial loss in domain differentiation, and cross-entropy loss in target domain information classification, we are able to reduce domain differences and achieve effective domain adaptation. We conducted experiments on three real CHD datasets, and the results show that our model outperforms existing single-domain network node classification methods and is able to distinguish well between high-risk CHD and low-risk CHD patient groups. This excellent predictive performance provides an aid to physicians in the diagnosis of cardiovascular problems.