A group theoretical approach to elasticity under constraints and predeformations

TL;DR

This paper introduces a group theoretical framework to address the complexities of nonlinear elasticity involving constraints and predeformations, providing generalized deformation measures and elastic moduli.

Contribution

It develops a novel group theory-based approach to define nonlinear shear deformation gradients and elastic moduli under constraints and predeformations.

Findings

Generalized definitions of shear deformation gradients.

Expressions for nonlinear elastic moduli.

Enhanced understanding of large deformations with constraints.

Abstract

Respecting deformational constraints and predeformations poses a substantial challenge in the description of nonlinear elasticity. We here outline how group theory can play a beneficial role to overcome this challenge. Specifically, group theory guides us to generalized definitions of nonlinear shear deformation gradients and expressions of generalized elastic moduli in the nonlinear regime. Particularly, such achievements become important in the context of larger deformations under constraints and additional deformations on top of predeformations.