Rheological Equations of Generalized Maxwell Model and Voigt Model in Three-Dimensional, Non-Linear Deformation.

Abstract

It is well known that the generalized Maxwell model and Voigt are very useful for description at the mechainical behaviours of the materials having the distribution of relaxation times or retardation times, as far as the deformation of the materials is one-dimensional and the strain and the strain rate are sufficiently small. In this paper, these two models have been extended so as to be applicable to three-dimensional and nonlinear deformations of initially isotropic materials and two sets of rheological equations corresponding to each of such extended models have been obtained. It has been also shown that, the condition of small deformation being introduced, each of the two sets are reduced to three-dimensional extensions of the corresponding classical equations, and moreover, the three-dimensionaly extended formulas, which are applied to simple elongation, are reduced to the corresponding classical (one-dimensional) equations for the case of simple elongation.