Phenomenological Theory of Visco-elasticity of Three Dimensional Bodies

Abstract

A phenomenological theory of the non-linear visco-elasticity of three dimensional bodies is presented. We start from the two elementary models of the classical linear theory of visco-elasticity, that is, the so-called Maxwell and Voigt models. These models are extended to three dimensional non-linear case by adopting the energy consideration. The three dimensional Maxwell model is defined by “series connection of a “non-Hookeian spring, i.e. the internal elastic mechanism and a “non-Newtonian dashpot the energy dissipation mechanism, and the three dimensional Voigt model is represented by the “parallel connection of these mechanisms. Making use of the Maxwell model, we discuss the tensile viscosity for the stationary simple elongation of elasticoviscous liquids. Our models are shown to be successful in analyzing the so-called normal stress effects, i.e., the Weissenberg effect for elastico-viscous liquids and the Poynting effect for visco-elastic solids. The non-linearity in visco-elastic properties i...