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A Total Lagrangian upwind Smooth Particle Hydrodynamics algorithm for large strain explicit solid dynamics / Antonio, Gil

Computer Methods in Applied Mechanics and Engineering, Volume: 344, Pages: 209 - 250

Swansea University Author: Antonio, Gil

Abstract

In previous work (Lee et al., 2016, 2017), Lee et al. introduced a new Smooth Particle Hydrodynamics (SPH) computational framework for large strain explicit solid dynamics with special emphasis on the treatment of near incompressibility. A first order system of hyperbolic equations was presented exp...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 00457825
Published: 2019
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URI: https://cronfa.swan.ac.uk/Record/cronfa44650
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first_indexed 2018-09-28T13:16:48Z
last_indexed 2018-11-19T20:21:46Z
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spelling 2018-11-19T16:27:30.6525163 v2 44650 2018-09-28 A Total Lagrangian upwind Smooth Particle Hydrodynamics algorithm for large strain explicit solid dynamics 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2018-09-28 EEN In previous work (Lee et al., 2016, 2017), Lee et al. introduced a new Smooth Particle Hydrodynamics (SPH) computational framework for large strain explicit solid dynamics with special emphasis on the treatment of near incompressibility. A first order system of hyperbolic equations was presented expressed in terms of the linear momentum and the minors of the deformation, namely the deformation gradient, its co-factor and its Jacobian. Taking advantage of this representation, the suppression of numerical deficiencies (e.g. spurious pressure, long term instability and/or consistency issues) was addressed through well-established stabilisation procedures. In Reference Lee et al. (2016), the adaptation of the very efficient Jameson-Schmidt-Turkel algorithm was presented. Reference Lee et al. (2017) introduced an adapted variationally consistent Streamline Upwind Petrov Galerkin methodology. In this paper, we now introduce a third alternative stabilisation strategy, extremely competitive, and which does not require the selection of any user-defined artificial stabilisation parameter. Specifically, a characteristic-based Riemann solver in conjunction with a linear reconstruction procedure is used, with the aim to guarantee both consistency and conservation of the overall algorithm. We show that the proposed SPH formulation is very similar in nature to that of the upwind vertex centred Finite Volume Method presented in Aguirre et al. (2015). In order to extend the application range towards the incompressibility limit, an artificial compressibility algorithm is also developed. Finally, an extensive set of challenging numerical examples is analysed. The new SPH algorithm shows excellent behaviour in compressible, nearly incompressible and truly incompressible scenarios, yielding second order of convergence for velocities, deviatoric and volumetric components of the stress. Journal Article Computer Methods in Applied Mechanics and Engineering 344 209 250 00457825 Conservation laws, SPH, Upwind, Riemann solver, Explicit dynamics, Incompressibility 1 1 2019 2019-01-01 10.1016/j.cma.2018.09.033 COLLEGE NANME Engineering COLLEGE CODE EEN Swansea University 2018-11-19T16:27:30.6525163 2018-09-28T09:50:09.8998416 College of Engineering Engineering Chun Hean Lee 1 Antonio Gil 0000-0001-7753-1414 2 Ataollah Ghavamian 3 Javier Bonet 4 0044650-18102018100227.pdf lee2018(5).pdf 2018-10-18T10:02:27.8300000 Output 24133436 application/pdf Accepted Manuscript true 2019-10-13T00:00:00.0000000 true eng
title A Total Lagrangian upwind Smooth Particle Hydrodynamics algorithm for large strain explicit solid dynamics
spellingShingle A Total Lagrangian upwind Smooth Particle Hydrodynamics algorithm for large strain explicit solid dynamics
Antonio, Gil
title_short A Total Lagrangian upwind Smooth Particle Hydrodynamics algorithm for large strain explicit solid dynamics
title_full A Total Lagrangian upwind Smooth Particle Hydrodynamics algorithm for large strain explicit solid dynamics
title_fullStr A Total Lagrangian upwind Smooth Particle Hydrodynamics algorithm for large strain explicit solid dynamics
title_full_unstemmed A Total Lagrangian upwind Smooth Particle Hydrodynamics algorithm for large strain explicit solid dynamics
title_sort A Total Lagrangian upwind Smooth Particle Hydrodynamics algorithm for large strain explicit solid dynamics
author_id_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2
author_id_fullname_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio, Gil
author Antonio, Gil
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container_title Computer Methods in Applied Mechanics and Engineering
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publishDate 2019
institution Swansea University
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doi_str_mv 10.1016/j.cma.2018.09.033
college_str College of Engineering
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hierarchy_top_title College of Engineering
hierarchy_parent_id collegeofengineering
hierarchy_parent_title College of Engineering
department_str Engineering{{{_:::_}}}College of Engineering{{{_:::_}}}Engineering
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description In previous work (Lee et al., 2016, 2017), Lee et al. introduced a new Smooth Particle Hydrodynamics (SPH) computational framework for large strain explicit solid dynamics with special emphasis on the treatment of near incompressibility. A first order system of hyperbolic equations was presented expressed in terms of the linear momentum and the minors of the deformation, namely the deformation gradient, its co-factor and its Jacobian. Taking advantage of this representation, the suppression of numerical deficiencies (e.g. spurious pressure, long term instability and/or consistency issues) was addressed through well-established stabilisation procedures. In Reference Lee et al. (2016), the adaptation of the very efficient Jameson-Schmidt-Turkel algorithm was presented. Reference Lee et al. (2017) introduced an adapted variationally consistent Streamline Upwind Petrov Galerkin methodology. In this paper, we now introduce a third alternative stabilisation strategy, extremely competitive, and which does not require the selection of any user-defined artificial stabilisation parameter. Specifically, a characteristic-based Riemann solver in conjunction with a linear reconstruction procedure is used, with the aim to guarantee both consistency and conservation of the overall algorithm. We show that the proposed SPH formulation is very similar in nature to that of the upwind vertex centred Finite Volume Method presented in Aguirre et al. (2015). In order to extend the application range towards the incompressibility limit, an artificial compressibility algorithm is also developed. Finally, an extensive set of challenging numerical examples is analysed. The new SPH algorithm shows excellent behaviour in compressible, nearly incompressible and truly incompressible scenarios, yielding second order of convergence for velocities, deviatoric and volumetric components of the stress.
published_date 2019-01-01T13:06:29Z
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score 10.873209