Rheological Equation of Voigtian Material

Abstract

In this paper, the well-known classical one-dimentional rheological equation of Voigtian material having a single retardation time is extended so as to be applicable to three-dimentional and large deformation, and Lagrange’s and Euler’s representations are explicitly used.
Our rheological equation in Euler’s representation is reduced to the most general stress-strain relation which was described by Rivlin and is derived by general procedure using the elastic theory of finite deformation, when its terms relating to viscosity are eliminated, and is reduced to the most general stress-strain rate relation which was derived by Reiner and Rivlin, when its terms relating to elasticity are omitted.
Then, the above equation is applied to simple elongation and simple shear, with satisfactory results.