A structurally frame-indifferent model for anisotropic visco-hyperelastic materials

TL;DR

This paper introduces a novel anisotropic remodelling equation for visco-hyperelastic materials that respects structural frame indifference, unifying fluid and solid behaviors through a dissipation-based model.

Contribution

It proposes a new anisotropic remodelling equation compatible with frame indifference, linking dissipative processes to elastic energy and dissipation densities.

Findings

Model reduces to Ericksen anisotropic fluid for slow deformations.

Model reduces to anisotropic hyperelastic solid for fast deformations.

Relaxation times significantly influence the constitutive response.

Abstract

One of the main theoretical issues in developing a theory of anisotropic viscoelastic media at finite strains lies in the proper definition of the material symmetry group and its evolution with time. In this paper the matter is discussed thoroughly and addressed by introducing a novel anisotropic remodelling equation compatible with the principle of structural frame indifference, a requirement that every inelastic theory based on the multiplicative decomposition of the deformation gradient must obey to. The evolution laws of the dissipative process are %obtained by introducing a novel (remodelling) balance equation which is completely determined by two scalar functions, the elastic strain energy and the dissipation densities. The proper choice of the dissipation function allows us to reduce the proposed model to the Ericksen anisotropic fluid, when deformation is sufficiently slow, or to the anisotropic hyperelastic solid for fast deformations. Finally, a few prototype examples are discussed to highlight the role of the relaxation times in the constitutive response.