TY - JOUR

T1 - Theoretical and numerical comparison of hyperelastic and hypoelastic formulations for Eulerian non-linear elastoplasticity

AU - Peshkov, Ilya

AU - Boscheri, Walter

AU - Loubère, Raphaël

AU - Romenski, Evgeniy

AU - Dumbser, Michael

N1 - Publisher Copyright: © 2019 Elsevier Inc.

PY - 2019/6/15

Y1 - 2019/6/15

N2 - 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.

AB - 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.

KW - Arbitrary high-order ADER Discontinuous Galerkin and Finite Volume schemes

KW - Direct ALE

KW - Path-conservative methods and stiff source terms

KW - Symmetric hyperbolic thermodynamically compatible systems (SHTC)

KW - Unified first order hyperbolic model of continuum mechanics

KW - Viscoplasticity and elastoplasticity

KW - DISCONTINUOUS GALERKIN SCHEMES

KW - ELEMENT-METHOD

KW - HIGH-ORDER

KW - Arbitrary high-order ADER Discontinuous

KW - PLASTIC FLOW

KW - RELATIVISTIC THERMODYNAMICS

KW - NONCONSERVATIVE HYPERBOLIC SYSTEMS

KW - ADER SCHEMES

KW - CONSERVATION-LAWS

KW - UNSTRUCTURED MESHES

KW - Galerkin and Finite Volume schemes

KW - FINITE-VOLUME SCHEMES

UR - http://www.scopus.com/inward/record.url?scp=85063501119&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2019.02.039

DO - 10.1016/j.jcp.2019.02.039

M3 - Article

AN - SCOPUS:85063501119

VL - 387

SP - 481

EP - 521

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -