An entropy-stable Smooth Particle Hydrodynamics algorithm for large strain thermo-elasticity

Ghavamian, A., Lee, C. H. , Gil, A. J., Bonet, J., Heuze, T. and Stainier, L. (2021) An entropy-stable Smooth Particle Hydrodynamics algorithm for large strain thermo-elasticity. Computer Methods in Applied Mechanics and Engineering, 379, 113736. (doi: 10.1016/j.cma.2021.113736)

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Abstract

This paper presents a novel Smooth Particle Hydrodynamics computational framework for the simulation of large strain fast solid dynamics in thermo-elasticity. The formulation is based on the Total Lagrangian description of a system of first order conservation laws written in terms of the linear momentum, the triplet of deformation measures (also known as minors of the deformation gradient tensor) and the total energy of the system, extending thus the previous work carried out by some of the authors in the context of isothermal elasticity and elasto-plasticity (Lee et al., 2016; Lee et al., 2017; Lee et al., 2019). To ensure the stability (i.e. hyperbolicity) of the formulation from the continuum point of view, the internal energy density is expressed as a polyconvex combination of the triplet of deformation measures and the entropy density. Moreover, and to guarantee stability from the spatial discretisation point of view, consistently derived Riemann-based numerical dissipation is carefully introduced where local numerical entropy production is demonstrated via a novel technique in terms of the time rate of the so-called ballistic free energy of the system. For completeness, an alternative and equally competitive formulation (in the case of smooth solutions), expressed in terms of the entropy density, is also implemented and compared. A series of numerical examples is presented in order to assess the applicability and robustness of the proposed formulations, where the Smooth Particle Hydrodynamics scheme is benchmarked against an alternative in-house Finite Volume Vertex Centred implementation.

Item Type:Articles
Additional Information:The authors would like to acknowledge the financial support received through the European Commission EACEA Agency, Framework Partnership Agreement 2013-0043 Erasmus Mundus Action 1b, as a part of the EM Joint Doctorate “Simulation in Engineering and Entrepreneurship Development (SEED)”. The second author gratefully acknowledges the support provided by the EPSRC, UK Strategic Support Package: Engineering of Active Materials by Multiscale/Multiphysics Computational Mechanics - EP/R008531/1. The third author acknowledges the financial support received through the European Training Network Protection (Project ID: 764636).
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Lee, Dr Chun Hean
Authors: Ghavamian, A., Lee, C. H., Gil, A. J., Bonet, J., Heuze, T., and Stainier, L.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Computer Methods in Applied Mechanics and Engineering
Publisher:Elsevier
ISSN:0045-7825
ISSN (Online):1879-2138
Published Online:09 March 2021
Copyright Holders:Copyright © 2021 Elsevier
First Published:First published in Computer Methods in Applied Mechanics and Engineering 379:113736
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
300129Strategic Support Package: Engineering of Active Materials by Multiscale/Multiphysics Computational MechanicsChristopher PearceEngineering and Physical Sciences Research Council (EPSRC)EP/R008531/1ENG - Infrastructure & Environment