Theoretical and numerical comparison of hyperelastic and hypoelastic formulations for Eulerian non-linear elastoplasticity

TL;DR

This paper compares hyperelastic and hypoelastic models for Eulerian non-linear elastoplasticity, analyzing conceptual differences and numerical solutions across various deformation scales using advanced computational methods.

Contribution

It provides a detailed theoretical and numerical comparison of hyperelastic and hypoelastic formulations, highlighting differences during large deformations.

Findings

Models agree for small elastic deformations

Differences increase with large elastoplastic deformations

Numerical methods effectively compare the two formulations

Abstract

The aim of this paper is to compare a hyperelastic with a hypoelastic model describing the Eulerian dynamics of solids in the context of non-linear elastoplastic deformations. Specifically, we consider the well-known hypoelastic Wilkins model, which is compared against a hyperelastic model based on the work of Godunov and Romenski. First, we discuss some general conceptual differences between the two approaches. Second, a detailed study of both models is proposed, where differences are made evident at the aid of deriving a hypoelastic-type model corresponding to the hyperelastic model and a particular equation of state used in this paper. Third, using the same high order ADER Finite Volume and Discontinuous Galerkin methods on fixed and moving unstructured meshes for both models, a wide range of numerical benchmark test problems has been solved. The numerical solutions obtained for the two different models are directly compared with each other. For small elastic deformations, the two models produce very similar solutions that are close to each other. However, if large elastic or elastoplastic deformations occur, the solutions present larger differences.