A new Jameson–Schmidt–Turkel Smooth Particle Hydrodynamics algorithm for large strain explicit fast dynamics

Lee, C. H. , Gil, A. J., Greto, G., Kulasegaram, S. and Bonet, J. (2016) A new Jameson–Schmidt–Turkel Smooth Particle Hydrodynamics algorithm for large strain explicit fast dynamics. Computer Methods in Applied Mechanics and Engineering, 311, pp. 71-111. (doi: 10.1016/j.cma.2016.07.033)

Abstract

This paper presents a new Smooth Particle Hydrodynamics (SPH) computational framework for large strain explicit solid dynamics. A mixed-based set of Total Lagrangian conservation laws (Bonet et al., 2015; Gil et al., 2016) is presented in terms of the linear momentum and an extended set of geometric strain measures, comprised of the deformation gradient, its co-factor and the Jacobian. Taking advantage of this representation, the main aim of this paper is the adaptation of the very efficient Jameson–Schmidt–Turkel (JST) algorithm (Jameson et al., 1981) extensively used in computational fluid dynamics, to a SPH based discretisation of the mixed-based set of conservation laws, with three key distinct novelties. First, a conservative JST-based SPH computational framework is presented with emphasis in nearly incompressible materials. Second, the suppression of numerical instabilities associated with the non-physical zero-energy modes is addressed through a well-established stabilisation procedure. Third, the use of a discrete angular momentum projection algorithm is presented in conjunction with a monolithic Total Variation Diminishing Runge–Kutta time integrator in order to guarantee the global conservation of angular momentum. For completeness, exact enforcement of essential boundary conditions is incorporated through the use of a Lagrange multiplier projection technique. A series of challenging numerical examples (e.g. in the near incompressibility regime) are examined in order to assess the robustness and accuracy of the proposed algorithm. The obtained results are benchmarked against a wide spectrum of alternative numerical strategies.

• Item Type: Articles
• Additional Information: The authors gratefully acknowledge the financial support provided by the Sêr Cymru National Research Network for Advanced Engineering and Materials, United Kingdom.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Lee, Dr Chun Hean
• Authors: Lee, C. H., Gil, A. J., Greto, G., Kulasegaram, S., and Bonet, J.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: Computer Methods in Applied Mechanics and Engineering
• Journal Abbr.: CMAME
• Publisher: Elsevier
• ISSN: 0045-7825
• ISSN (Online): 1879-2138
• Published Online: 03 August 2016
• Copyright Holders: Copyright © 2016 Elsevier B.V.
• First Published: First published in Computer Methods in Applied Mechanics and Engineering 311: 71-111
• Publisher Policy: Reproduced in accordance with the publisher copyright policy