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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:387

Article

Peshkov, Ilya^1,4  Boscheri, Walter²  Loubere, Raphael³  Romenski, Evgeniy^4,5,6  Dumbser, Michael⁶ 

[1] Univ Toulouse 3, Inst Math Toulouse, F-31062 Toulouse, France

[2] Univ Ferrara, Dept Math & Comp Sci, Via Machiavelli 30, I-44121 Ferrara, Italy

[3] Univ Bordeaux, IMB, UMR 5219, F-33405 Talence, France

[4] Sobolev Inst Math, 4 Acad Koptyug Ave, Novosibirsk 630090, Russia

[5] Novosibirsk State Univ, 2 Pirogova Str, Novosibirsk 630090, Russia

[6] Univ Trento, Dept Civil Environm & Mech Engn, Via Mesiano 77, I-38123 Trento, Italy

关键词: Symmetric hyperbolic thermodynamically compatible systems (SHTC);    Unified first order hyperbolic model of continuum mechanics;    Viscoplasticity and elastoplasticity;    Arbitrary high-order ADER Discontinuous;    Galerkin and Finite Volume schemes;    Path-conservative methods and stiff source terms;    Direct ALE;   

DOI  :  10.1016/j.jcp.2019.02.039

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free