An acoustic Riemann solver for large strain computational contact dynamics

Runcie, C. J., Lee, C. H. , Haider, J., Gil, A. J. and Bonet, J. (2022) An acoustic Riemann solver for large strain computational contact dynamics. International Journal for Numerical Methods in Engineering, 123(23), pp. 5700-5748. (doi: 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 (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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Runcie, Mr Callum and Lee, Dr Chun Hean
• Authors: Runcie, C. J., Lee, C. H., Haider, J., Gil, A. J., and Bonet, J.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: International Journal for Numerical Methods in Engineering
• Publisher: Wiley
• ISSN: 0029-5981
• ISSN (Online): 1097-0207
• Published Online: 05 August 2022
• Copyright Holders: Copyright © 2022 The Authors
• First Published: First published in International Journal for Numerical Methods in Engineering 123(23): 5700-5748
• Publisher Policy: Reproduced under a Creative Commons License

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
300129		Strategic Support Package: Engineering of Active Materials by Multiscale/Multiphysics Computational Mechanics	Christopher Pearce	Engineering and Physical Sciences Research Council (EPSRC)	EP/R008531/1	ENG - Infrastructure & Environment