The exponentiated Hencky energy: Anisotropic extension and case studies

TL;DR

This paper extends the isotropic exponentiated Hencky elastic energy to anisotropic materials using logarithmic strain invariants and structural tensors, supported by case studies.

Contribution

It introduces a novel anisotropic extension of the exponentiated Hencky energy based on geometric principles and strain invariants.

Findings

Successful formulation of anisotropic energy model

Application to selected case studies demonstrating effectiveness

Provides a geometric foundation for anisotropic elasticity

Abstract

In this paper we propose an anisotropic extension of the isotropic exponentiated Hencky energy, based on logarithmic strain invariants. Unlike other elastic formulations, the isotropic exponentiated Hencky elastic energy has been derived solely on differential geometric grounds, involving the geodesic distance of the deformation gradient F to the group of rotations. We formally extend this approach towards anisotropy by defining additional anisotropic logarithmic strain invariants with the help of suitable structural tensors and consider our findings for selected case studies.