Finite Linear Viscoelasticity

Abstract

Simple finite strain versions of the Maxwell and Kelvin‐Voigt viscoelastic solids are investigated within the framework of continuum mechanics. Three‐dimensional constitutive equations are examined with two different measures of the strain‐rate tensor: the standard Eulerian strain rate and the Jaumann rate of the logarithmic strain tensor. The analysis centers on examining the basic deformation patterns of simple shear and uniaxial tension. A detailed comparison is made among the theoretical predictions obtained from the different material models. These are based on exact analytical solutions of the field equations. The choice of the strain‐rate measure is shown to have an appreciable effect on the stress field in simple shear, particularly for large strains. Also discussed is the role of elastic compressibility in uniaxial tension, including the area relaxation phenomena for the Maxwell solids under constant stretch. A further example is given for nonlinear viscous materials—in conjunction with the pure power law—in simple shear. The results of this study indicate the possible applicability of various rates of strain tensors in constructing viscoelastic models.