A Definition of Plasticity
THE word ‘plasticity’, although one which has attained a state almost of ubiquity in several branches of applied physics and industrial chemistry, has, according to Scott Blair1, never been given a quantitative and dimensional definition. In the technical literature a group of quantitative ‘plasticity numbers’ have taken their place. Such expressions as the Williams plasticity number, or the Goodrich plasticity number (both used in rubber technology), have no quantitative meaning other than that of the reading of a particular type of testing equipment when used in a particular manner, and as such cannot be expressed in C.G.S. units.
Constitutive behavior modeling and fractional derivatives
Publisher Summary This chapter reveals that fractional calculus allows a physically sound generalization of classical models from the linear theory of viscoelasticity. From a mathematical point of view, the operation of fractional integrodifferentiation is well defined and can be easily handled in Fourier or Laplace space. Integrodifferentiation allows, for instance, to interpolate smoothly between Hooke's and Newton's laws. The simplest form of a fractional rheological model is introduced, that is, fractional element (FE), and several mechanical analogs are presented, namely arrangements made out of springs and dashpots. In these (infinite) networks the order of fractional integration or differentiation can be adjusted in several ways; such as, by varying the material constants of the springs and dashpots involved, or by changing the structure of the arrangement. It is shown that parallel or serial combinations of FEs lead to more complex models; in particular, the extensions of the Maxwell, the Kelvin-Voigt, the Zener and the Poynting-Thomson models are studied. The representation of generalized viscoelastic models by fractional analogues also allows a deeper insight into the physics behind fractional stress-strain relations.
Use of laser scanning confocal microscopy for morphological taxonomy and the potential for digital type specimens (e-types)
The use of laser scanning confocal microscopy (LSCM) for creating taxonomic descriptions of copepods is investigated. A new technique is described, which employs a contour filter to process digital LSCM images, allowing taxonomic information to be quickly and accu- rately distilled into a simple illustration. LSCM allows the imaging of whole specimens, which can be rotated and viewed from any angle—a major benefit over light microscopy. Using this tech- nique, it is suggested that taxonomic descriptions can be rapidly produced in a fraction of the time required to produce similar descriptions using traditional light microscopy and hand drawing techniques. Good staining of specimens is, however, essential to produce accurate descriptions and more research is required in this area. The use of LSCM for morphological taxonomy shows great potential, not only for producing taxonomic descriptions, but also providing a comple - mentary adjunct to traditional type specimens in the form of 3D digital 'e-types' deposited in recognised international databases.