Model for a linear viscoelastic medium that has consistent creep and stress‐relaxation properties

Abstract

The stress and strain tensors for a homogeneous isotropic viscoelastic material are related by a general linear transformation, which expresses a complete proportionality of the sum of the stress and the stress‐rate fields to the sum of the strain and the strain‐rate fields in the medium. This transformation defines the functional forms of all components in the symmetric fourth‐rank matter tensors that specify the stiffness and the compliance of the dissipative medium. Corresponding stiffness and compliance moduli (e.g., shear modulus and shear compliance) are found to have the same kind of functional dependence upon the frequency. Thus the stress‐relaxation effects exhibited by the any stiffness modulus are consistent with the creep (strain‐relaxation) effects exhibited by the corresponding compliance modulus. However, ass consequence of the tensor relation between stress and strain, stiffness (and compliance) moduli of different kinds (e.g., shear modulus and bulk modulus) vary with frequency in different ways. The matrix forms of the stiffness and compliance tensors are discussed in terms of analogous equivalent networks that can be used to represent the mechanical behavior of the viscoelastic medium. Tensor transformations and network‐analysis algebra were carried out using computer programs for symbol manipulation.