The state of stress and strain adjacent to notches in a new class of nonlinear elastic bodies

TL;DR

This study investigates stress and strain near notches in a new class of nonlinear elastic bodies, modeled via implicit constitutive relations, with numerical solutions analyzing stability and convergence.

Contribution

It introduces a novel approach to modeling elastic bodies with notches using implicit constitutive relations, specifically for metallic alloys like gum metal.

Findings

Numerical solutions demonstrate stable and convergent stress-strain fields near notches.

The models effectively describe stress concentration effects in nonlinear elastic materials.

The approach provides insights into deformation behavior in advanced metallic alloys.

Abstract

In this paper we study the deformation of a body with a notch subject to an anti-plane state of stress within the context of a new class of elastic models. These models stem as approximations of constitutive response functions for an elastic body that is defined within the context of an implicit constitutive relation between the stress and the deformation gradient. Gum metal and many metallic alloys are described well by such constitutive relations. We consider the state of anti-plane stress of a body with a smoothened V-notch within the context of constitutive relations for the linearized strain in terms of a power-law for the stretch. The problem is solved numerically and the convergence and the stability of the solution is studied.