A generalization of the Kelvin–Voigt model with pressure‐dependent moduli in which both stress and strain appear linearly

Abstract

A generalization of the Kelvin–Voigt model that can represent viscoelastic materials whose moduli depend on the mechanical pressure is derived from an implicit constitutive relation in which both the Cauchy stress and the linearized strain appear linearly. For consistency with the assumption of small deformation, a thresholding approach is applied. The proposed mixed variational problem is investigated for its well‐posedness within the context of maximal monotone and coercive graphs. For isotropic extension or compression, a semi‐analytic solution of the generalization of the Kelvin–Voigt problem under stress control is presented. The corresponding numerical simulation for monotone and cyclic pressure loading is carried out, and the results then compared against the linearized model.