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.

Theoretical and numerical comparison of hyperelastic and hypoelastic formulations for Eulerian non-linear elastoplasticity / Peshkov, I.; Boscheri, W.; Loubere, R.; Romenski, E.; Dumbser, M.. - In: JOURNAL OF COMPUTATIONAL PHYSICS. - ISSN 0021-9991. - 387:(2019), pp. 481-521. [10.1016/j.jcp.2019.02.039]

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

Peshkov I.;Boscheri W.;Dumbser M.
2019-01-01

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.
2019
Peshkov, I.; Boscheri, W.; Loubere, R.; Romenski, E.; Dumbser, M.
Theoretical and numerical comparison of hyperelastic and hypoelastic formulations for Eulerian non-linear elastoplasticity / Peshkov, I.; Boscheri, W.; Loubere, R.; Romenski, E.; Dumbser, M.. - In: JOURNAL OF COMPUTATIONAL PHYSICS. - ISSN 0021-9991. - 387:(2019), pp. 481-521. [10.1016/j.jcp.2019.02.039]
File in questo prodotto:
File Dimensione Formato  
1_Peshkov_Theoretical_1-s2.0-S0021999119301561-main.pdf

Solo gestori archivio

Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 6.4 MB
Formato Adobe PDF
6.4 MB Adobe PDF   Visualizza/Apri
2_Peshkov_Theoretical_1-s2.0-S0021999119301561-main.pdf

Solo gestori archivio

Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 6.04 MB
Formato Adobe PDF
6.04 MB Adobe PDF   Visualizza/Apri
Theoretical and numerical.pdf

accesso aperto

Tipologia: Pre-print non referato (Non-refereed preprint)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 6.89 MB
Formato Adobe PDF
6.89 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/286931
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 31
  • ???jsp.display-item.citation.isi??? 30
  • OpenAlex ND
social impact