An Eulerian method for multi-component problems in non-linear elasticity with sliding interfaces

P.T. Barton, D. Drikakis

Research output: Contribution to journalArticle

36 Citations (Scopus)

Abstract

This paper is devoted to developing a multi-material numerical scheme for non-linear elastic solids, with emphasis on the inclusion of interfacial boundary conditions. In particular for colliding solid objects it is desirable to allow large deformations and relative slide, whilst employing fixed grids and maintaining sharp interfaces. Existing schemes utilising interface tracking methods such as volume-of-fluid typically introduce erroneous transport of tangential momentum across material boundaries. Aside from combatting these difficulties one can also make improvements in a numerical scheme for multiple compressible solids by utilising governing models that facilitate application of high-order shock capturing methods developed for hydrodynamics. A numerical scheme that simultaneously allows for sliding boundaries and utilises such high-order shock capturing methods has not yet been demonstrated. A scheme is proposed here that directly addresses these challenges by extending a ghost cell method for gas-dynamics to solid mechanics, by using a first-order model for elastic materials in conservative form. Interface interactions are captured using the solution of a multi-material Riemann problem which is derived in detail. Several different boundary conditions are considered including solid/solid and solid/vacuum contact problems. Interfaces are tracked using level-set functions. The underlying single material numerical method includes a characteristic based Riemann solver and high-order WENO reconstruction. Numerical solutions of example multi-material problems are provided in comparison to exact solutions for the one-dimensional augmented system, and for a two-dimensional friction experiment.
LanguageEnglish
Pages5518-5540
Number of pages23
JournalJournal of Computational Physics
Volume229
Issue number15
DOIs
Publication statusPublished - 1 Aug 2010

Fingerprint

sliding
Elasticity
elastic properties
shock
solid mechanics
boundary conditions
Boundary conditions
Cauchy problem
gas dynamics
ghosts
Gas dynamics
chutes
friction
hydrodynamics
grids
Numerical methods
Momentum
inclusions
Mechanics
Hydrodynamics

Keywords

  • Riemann problem
  • level-set method
  • ghost fluid method
  • solid mechanics
  • non-linear elasticity
  • WENO
  • Eulerian method

Cite this

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abstract = "This paper is devoted to developing a multi-material numerical scheme for non-linear elastic solids, with emphasis on the inclusion of interfacial boundary conditions. In particular for colliding solid objects it is desirable to allow large deformations and relative slide, whilst employing fixed grids and maintaining sharp interfaces. Existing schemes utilising interface tracking methods such as volume-of-fluid typically introduce erroneous transport of tangential momentum across material boundaries. Aside from combatting these difficulties one can also make improvements in a numerical scheme for multiple compressible solids by utilising governing models that facilitate application of high-order shock capturing methods developed for hydrodynamics. A numerical scheme that simultaneously allows for sliding boundaries and utilises such high-order shock capturing methods has not yet been demonstrated. A scheme is proposed here that directly addresses these challenges by extending a ghost cell method for gas-dynamics to solid mechanics, by using a first-order model for elastic materials in conservative form. Interface interactions are captured using the solution of a multi-material Riemann problem which is derived in detail. Several different boundary conditions are considered including solid/solid and solid/vacuum contact problems. Interfaces are tracked using level-set functions. The underlying single material numerical method includes a characteristic based Riemann solver and high-order WENO reconstruction. Numerical solutions of example multi-material problems are provided in comparison to exact solutions for the one-dimensional augmented system, and for a two-dimensional friction experiment.",
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An Eulerian method for multi-component problems in non-linear elasticity with sliding interfaces. / Barton, P.T.; Drikakis, D.

In: Journal of Computational Physics, Vol. 229, No. 15, 01.08.2010, p. 5518-5540.

Research output: Contribution to journalArticle

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