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.
Outline of a Systematic Survey of Rheological Theories
The theories which have been proposed in order to explain rheological phenomena have increased to such an extent that it is difficult to avoid confusion. Some of these theories appear to be conflicting, although they may be equally correct, each one in its own field. For this reason a systematic survey of rheological theories should be very useful. It should make understanding the different theories more easy and it should assist in assessing to each of them its value in its proper field.