A Theory of Viscoelasticity of Finite Deformation as a Similar-Type Extenstion of the Nonlinear Elasticity Theory

Abstract

A nonlinear theory of viscoelasticity of finite deformation is developed on the basis of the analytical system of approximation in the elasticity theory of finite deformation, which was re-examined and organized in Part I. The theory is derived from the elasticity theory by introducing a series of multi-time memory functions for taking account of the time dependence of viscoelasticity. There exists one-to-one correspondence between the constitutive equations in the elasticity theory and those in the present theory; the former being just like a map from the latter. The simple, plain, and concrete characters of the elasticity theory are thus inherited by the present theory, and a fortune of the elasticity theory such as ample approaches to the three dimensional analysis and accumulations of data become available for the analysis of viscoelasticity. The present theory may be valid for the analysis of deviation from the elasticity theory due to viscoelasticity and from the theory of linear viscoelasticity due to non-linearity. The theory gives the constitutive equations which corresponds to the equations of the Oth-order to the 2nd-order (Guth-Wang's approximation) in the molecular network theory of rubberlike elasticity. This suggests that the present theory may be useful for further construction of molecula theory of finite nonlinear viscoelasticity of rubberlike materials.