Solution of viscoelastic creep models for anisotropic materials with linear relation between strain and stress but nonlinear with respect to time

Abstract

In this paper, we investigate anisotropic viscoelastic materials describing (both) creep relaxation and aging. The constitutive response is presented by hereditary integrals with memory kernel matrices using the Voigt–Mandel algebra. When the entries of the memory matrix are proportional with respect to time scale, a viscoelastic solution is constructed based on the variational solution of the corresponding anisotropic linear elastic problem. Example equations are presented, e.g., for orthotropic elastic materials, for standard linear solid (Zener) and Burgers viscoelastic models.

Keywords

• Viscoelasticity
• Anisotropic material
• Creep
• Volterra integral
• Variational equation