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

Ilya Peshkov, Walter Boscheri, Raphaël Loubère, Evgeniy Romenski, Michael Dumbser

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)

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 of 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.

Original languageEnglish
Pages (from-to)481-521
Number of pages41
JournalJournal of Computational Physics
Volume387
DOIs
Publication statusPublished - 15 Jun 2019

Keywords

  • Arbitrary high-order ADER Discontinuous Galerkin and Finite Volume schemes
  • Direct ALE
  • Path-conservative methods and stiff source terms
  • Symmetric hyperbolic thermodynamically compatible systems (SHTC)
  • Unified first order hyperbolic model of continuum mechanics
  • Viscoplasticity and elastoplasticity
  • DISCONTINUOUS GALERKIN SCHEMES
  • ELEMENT-METHOD
  • HIGH-ORDER
  • Arbitrary high-order ADER Discontinuous
  • PLASTIC FLOW
  • RELATIVISTIC THERMODYNAMICS
  • NONCONSERVATIVE HYPERBOLIC SYSTEMS
  • ADER SCHEMES
  • CONSERVATION-LAWS
  • UNSTRUCTURED MESHES
  • Galerkin and Finite Volume schemes
  • FINITE-VOLUME SCHEMES

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