This research presents a deep learning based approach to predict stress fields in the solid material elastic deformation using convolutional neural networks (CNN). Two different architectures are proposed to solve the problem. One is Feature Representation embedded Convolutional Neural Network (FR-CNN) with a single input channel, and the other is Squeeze-and-Excitation Residual network modules embedded Fully Convolutional Neural network (SE-Res-FCN) with multiple input channels. Both the tow architectures are stable and converged reliably in training and testing on GPUs. Accuracy analysis shows that SE-Res-FCN has a significantly smaller mean squared error (MSE) and mean absolute error (MAE) than FR-CNN. Mean relative error (MRE) of the SE-Res-FCN model is about 0.25 with respect to the average ground truth. The validation results indicate that the SE-Res-FCN model can accurately predict the stress field. For stress field prediction, the hierarchical architecture becomes deeper within certain limits, and then its prediction becomes more accurate. Fully trained deep learning models have higher computational efficiency over conventional FEM models, so they have great foreground and potential in structural design and topology optimization.
The Artificial Neural Networks (ANN) with the multilayer perceptron (MLP) has been applied in computational mechanics for several years, for structural analysis @cite_23 @cite_4 @cite_33 , materials failure and damage @cite_2 @cite_28 @cite_1 @cite_32 , regression of the material constitutive properties @cite_2 @cite_34 @cite_15 @cite_11 @cite_16 , computational mechanics enhancement @cite_38 @cite_29 , topological design and optimization @cite_36 @cite_24 . However, due to the intrinsic limitation of MLP, the geometry is usually abstracted and simplified into a feature vector that loses the spatial position relationship, making the approach difficult to generalize to complex cases.
@cite_38 @cite_4 @cite_33 @cite_28 @cite_36 @cite_29 @cite_1 @cite_32 @cite_16 @cite_24 @cite_23 @cite_2 @cite_15 @cite_34 @cite_11
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Abstract The present paper describes a method to enhance the capability of, or to broaden the scope of computational mechanics by using deep learning, which is one of the machine learning methods and is based on the artificial neural network. The method utilizes deep learning to extract rules inherent in a computational mechanics application, which usually are implicit and sometimes too complicated to grasp from the large amount of available data A new method of numerical quadrature for the FEM stiffness matrices is developed by using the proposed method, where a kind of optimized quadrature rule superior in accuracy to the standard Gauss–Legendre quadrature is obtained on the element-by-element basis. The detailed formulation of the proposed method is given with the sample application above, and an acceleration technique for the proposed method is discussed Abstract Basic ideas of back-propagation neural networks (BPNNs) are presented in short. Then BPNN applications in analysis of the following problems are discussed: (1) bending analysis of elastoplastic beams, (2) elastoplastic plane stress problem, (3) estimation of fundamental vibration periods of real buildings, (4) detection of damage in a steel beam, (5) identification of loads applied to an elastoplastic beam. Regularization neural network is briefly discussed and its application to estimation of concrete fatigue durability it shown. A modified Hopfield network is used to the analysis of an elastic angular plate with unilateral constraints. In the end some conclusions and prospects of neurocomputing applications are pointed out. Abstract Damage to structures may be caused as a result of normal operations, accidents, deterioration or severe natural events such as earthquakes and storms. Most often the extent and the location of the damage can be determined through visual inspection. However, in some cases visual inspection may not be feasible. The study reported in this paper is the first stage of a research aimed at developing automatic monitoring methods for detection of structural damage. In this feasibility study we have explored the use of the self-organization and learning capabilities of neural networks in structural damage assessment. The basic strategy is to train a neural network to recognize the behavior of the undamaged structure as well as the behavior of the structure with various possible damage states. When the trained network is subjected to the measurements of the structural response, it should be able to detect any existing damage. We have tried this basic idea on a simple structure and the results are promising. Training Deep Neural Networks is complicated by the fact that the distribution of each layer's inputs changes during training, as the parameters of the previous layers change. This slows down the training by requiring lower learning rates and careful parameter initialization, and makes it notoriously hard to train models with saturating nonlinearities. We refer to this phenomenon as internal covariate shift, and address the problem by normalizing layer inputs. Our method draws its strength from making normalization a part of the model architecture and performing the normalization for each training mini-batch. Batch Normalization allows us to use much higher learning rates and be less careful about initialization. It also acts as a regularizer, in some cases eliminating the need for Dropout. Applied to a state-of-the-art image classification model, Batch Normalization achieves the same accuracy with 14 times fewer training steps, and beats the original model by a significant margin. Using an ensemble of batch-normalized networks, we improve upon the best published result on ImageNet classification: reaching 4.9 top-5 validation error (and 4.8 test error), exceeding the accuracy of human raters. This paper deals with structural damage detection using measured frequency response functions (FRFs) as input data to artificial neural networks (ANNs). A major obstacle, the impracticality of using full-size FRF data with ANNs, was circumvented by applying a principal component analysis (PCA)-based data reduction technique to the measured FRFs. The compressed FRFs, represented by their projection onto the most significant principal components, were then used as the ANN input variables instead of the raw FRF data. The output is a prediction for the actual state of the specimen, i.e., healthy or damaged. A further advantage of this particular approach was found to be the ability to deal with relatively high measurement noise, which is of common occurrence when dealing with industrial structures. The methodology was applied to the measured FRFs of a railway wheel, each response function having 4096 spectral lines. The available FRF data were grouped into x, y and z direction FRFs and a compression ratio of about 400 was achieved for each direction. Three different networks, each corresponding to a co-ordinate direction, were trained and verified using 80 PCA-compressed FRFs. Twenty compressed FRFs, obtained from further measurements, were used for the actual damage detection tests. Half of the test FRFs were polluted further by adding 5 random noise in order to assess the robustness of the method in the presence of significant experimental noise. The results showed that, in all cases considered, it was possible to distinguish between the healthy and damaged states with very good accuracy and repeatability. Abstract The patient-specific biomechanical analysis of the aorta requires the quantification of the in vivo mechanical properties of individual patients. Current inverse approaches have attempted to estimate the nonlinear, anisotropic material parameters from in vivo image data using certain optimization schemes. However, since such inverse methods are dependent on iterative nonlinear optimization, these methods are highly computation-intensive. A potential paradigm-changing solution to the bottleneck associated with patient-specific computational modeling is to incorporate machine learning (ML) algorithms to expedite the procedure of in vivo material parameter identification. In this paper, we developed an ML-based approach to estimate the material parameters from three-dimensional aorta geometries obtained at two different blood pressure (i.e., systolic and diastolic) levels. The nonlinear relationship between the two loaded shapes and the constitutive parameters is established by an ML-model, which was trained and tested using finite element (FE) simulation datasets. Cross-validations were used to adjust the ML-model structure on a training validation dataset. The accuracy of the ML-model was examined using a testing dataset. This paper describes an approach to identify plastic deformation and failure properties of ductile materials. The experimental method of the small punch test is used to determine the material response under loading. The resulting load displacement curve is transferred to a neural network, which was trained using load displacement curves generated by finite element simulations of the small punch test and the corresponding material parameters. The simulated material behavior of the specimen is based on the ductile elastoplastic damage theory of Gurson, Tvergaard and Needleman. During a training process the neural network generates an approximated function for the inverse problem relating the material parameters to the shape of the load displacement curve of the small punch test. This technique was tested for three different materials (ductile steels). The identified parameters are verified by testing and simulating notched tensile specimens. Abstract We consider materials which can be described by plasticity laws exhibiting nonlinearkinematic and nonlinear isotropic hardening effects. The aim is to show that the materialparameters governing the constitutive behavior may be determined from data obtained byspherical indentation. Note that only the measurable global quantities (load and indentationdepth) should be utilized, which are available, e.g. from depth-sensing indentation tests. For thisgoal use is made of the method of neural networks. The developed neural networks apply also tothe case of pure kinematic as well as pure isotropic hardening. Moreover it is shown how amonotonic strain–stress curve can be assigned to the spherical indentation test. Abstract This article presents an approach to use neural networks as a constitutive model for the inelastic deformation behavior of open-cell foams or other porous materials. The inelastic deformation behavior of highly porous materials can be very complex and makes the formulation of a closed form constitutive model a very challenging or even impossible task. The presented methods include the creation of a periodic representative volume element (RVE) of the porous structure, the supply of training data by means of finite element simulations using the RVE and the use of trained neural networks within a user material routine (UMAT) for the finite element code ABAQUS . As a proof of concept this approach is applied to relatively simple two dimensional porous structures, where both the homogenized material behavior and a fully resolved porous structure are simulated and compared. The computational effort for simulating a simple foam structure can be reduced by a factor of more than 10,000 using the proposed homogenization approach.