Research output: Contribution to journal › Article › peer-review
Theoretical and numerical comparison of hyperelastic and hypoelastic formulations for Eulerian non-linear elastoplasticity. / Peshkov, Ilya; Boscheri, Walter; Loubère, Raphaël et al.
In: Journal of Computational Physics, Vol. 387, 15.06.2019, p. 481-521.Research output: Contribution to journal › Article › peer-review
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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 -
ID: 19039188