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An acoustic Riemann solver for large strain computational contact dynamics

Callum J. Runcie, Chun Hean Lee Orcid Logo, Jibran Haider, Antonio Gil Orcid Logo, Javier Bonet

International Journal for Numerical Methods in Engineering, Volume: 123, Issue: 23, Pages: 5700 - 5748

Swansea University Authors: Chun Hean Lee Orcid Logo, Antonio Gil Orcid Logo

  • Accepted Manuscript under embargo until: 5th August 2023

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DOI (Published version): 10.1002/nme.7085

Abstract

This paper presents a vertex-centred finite volume algorithm for the explicit dynamic analysis of large strain contact problems. The methodology exploits the use of a system of first order conservation equations written in terms of the linear momentum and a triplet of geometric deformation measures...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 0029-5981 1097-0207
Published: Wiley 2022
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URI: https://cronfa.swan.ac.uk/Record/cronfa60808
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Abstract: This paper presents a vertex-centred finite volume algorithm for the explicit dynamic analysis of large strain contact problems. The methodology exploits the use of a system of first order conservation equations written in terms of the linear momentum and a triplet of geometric deformation measures (comprising the deformation gradient tensor, its co-factor and its Jacobian) together with their associated jump conditions. The latter can be used to derive several dynamic contact models ensuring the preservation of hyperbolic characteristic structure across solution discontinuities at the contact interface, a clear advantage over the standard quasi-static contact models where the influence of inertial effects at the contact interface is completely neglected. Taking advantage of the conservative nature of the formalism, both kinetic (traction) and kinematic (velocity) contact interface conditions are explicitly enforced at the fluxes through the use of appropriate jump conditions. Specifically, the kinetic condition is enforced in the usual linear momentum equation, whereas the kinematic condition can now be easily enforced in the geometric conservation equations without requiring a computationally demanding iterative algorithm. Additionally, a Total Variation Diminishing shock capturing technique can be suitably incorporated in order to improve dramatically the performance of the algorithm at the vicinity of shocks. Moreover, and to guarantee stability from the spatial discretisation standpoint, global entropy production is demonstrated through the satisfaction of semi-discrete version of the classical Coleman–Noll procedure expressed in terms of the time rate of the so-called Hamiltonian energy of the system. Finally, a series of numerical examples is examined in order to assess the performance and applicability of the algorithm suitably implemented in OpenFOAM. The knowledge of the potential contact loci between contact interfaces is assumed to be known a priori.
Keywords: Explicit contact dynamics, Conservation laws, large strain, Riemann solver, OpenFOAM, Shocks
College: Faculty of Science and Engineering
Funders: Runcie and Lee gratefully acknowledge the support provided by the EPSRC Strategic SupportPackage: Engineering of Active Materials by Multiscale/Multiphysics Computational Mechan-ics - EP/R008531/1. Gil and Lee would like to acknowledge the financial support receivedthrough the project Marie Sk lodowska-Curie ITN-EJD ProTechTion, funded by the EuropeanUnion Horizon 2020 research and innovation program with grant number 764636.
Issue: 23
Start Page: 5700
End Page: 5748