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

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

Journal

Journal of Computational Physics
ISSN: 0021-9991 , E-ISSN: 1090-2716

Output data

Year: 2019, Volume: 387, Pages: 481-521 Pages count : 41 DOI: 10.1016/j.jcp.2019.02.039

Tags

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

Authors

Peshkov I. ^1,4 , Boscheri W. ² , Loubère R. ³ , Romenski E. ^4,5,6 , Dumbser M. ⁶

Affiliations

1	Institut de Mathématiques de Toulouse, Université Toulouse III, Toulouse, F-31062, France
2	Department of Mathematics and Computer Science, University of Ferrara, Via Machiavelli 30, Ferrara, 44121, Italy
3	Institut de Mathématiques de Bordeaux (IMB), UMR 5219, Université de Bordeaux, Talence, F-33405, France
4	Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, Novosibirsk, 630090, Russian Federation
5	Novosibirsk State University, 2 Pirogova Str., Novosibirsk, 630090, Russian Federation
6	Department of Civil, Environmental and Mechanical Engineering, University of Trento, Via Mesiano 77, Trento, 38123, Italy

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. © 2019 Elsevier Inc.

Peshkov I. , Boscheri W. , Loubère R. , Romenski E. , Dumbser M.
Theoretical and numerical comparison of hyperelastic and hypoelastic formulations for Eulerian non-linear elastoplasticity
Journal of Computational Physics. 2019. V.387. P.481-521. DOI: 10.1016/j.jcp.2019.02.039 WOS Scopus OpenAlex

Web of science:	WOS:000465436700023
Scopus:	2-s2.0-85063501119
OpenAlex:	W2807528150

DB	Citing
Scopus	36
OpenAlex	49
Web of science	34