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A novel Arbitrary Lagrangian Eulerian Smooth Particle Hydrodynamics algorithm for nonlinear solid dynamics

Chun Hean Lee, Antonio Gil Orcid Logo, Paulo Refachinho De Campos, Javier Bonet, Tadas Jaugielavicius, Shreyas Joshi, Clare Wood Orcid Logo

Computer Methods in Applied Mechanics and Engineering, Volume: 427, Start page: 117055

Swansea University Authors: Antonio Gil Orcid Logo, Paulo Refachinho De Campos, Clare Wood Orcid Logo

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DOI (Published version): 10.1016/j.cma.2024.117055

Abstract

This paper introduces a novel Smooth Particle Hydrodynamics (SPH) computational framework that incorporates an Arbitrary Lagrangian Eulerian (ALE) formalism, expressed through a system of first-order conservation laws. In addition to the standard material and spatial configurations, an additional (f...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825
Published: Elsevier BV 2024
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In addition to the standard material and spatial configurations, an additional (fixed) referential configuration is introduced. The ALE conservative framework is established based on the fundamental conservation principles, including mass, linear momentum and the first law of thermodynamics represented through entropy density. A key contribution of this work lies in the evaluation of the physical deformation gradient tensor, which measures deformation from material to spatial configuration through a multiplicative decomposition into two auxiliary deformation gradient tensors. Both of the deformation tensors are obtained via additional first-order conservation equations. Interestingly, the new ALE conservative formulation will be shown to degenerate into alternative mixed systems of conservation laws for solid dynamics: particle-shifting, velocity-shifting and Eulerian formulations. The framework also considers path- and/or strain rate-dependent constitutive models, such as isothermal plasticity and thermo-visco-plasticity, by integrating evolution equations for internal state variables. Another contribution of this paper is the evaluation of ALE motion (known as smoothing procedure) by solving a conservation-type momentum equation. This procedure is indeed useful for maintaining a regular particle distribution and enhancing solution accuracy in regions characterised by large plastic flows. The hyperbolicity of the underlying system is ensured and accurate wave speed bounds in the context of ALE description are presented, crucial for ensuring the stability of explicit time integrators. For spatial discretisation, a Godunov-type SPH method is employed and adapted. To guarantee stability from the semi-discretisation standpoint, a carefully designed numerical stabilisation is introduced. The Lyapunov stability analysis is carried out by assessing the time rate of the Ballistic energy of the system, aiming to ensure non-negative entropy production. In order to ensure the global conservation of angular momentum, we employ a three-stage Runge&#x2013;Kutta time integrator together with a discrete angular momentum projection algorithm. Finally, a range of three dimensional benchmark problems are examined to illustrate the robustness and applicability of the framework. 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spelling 2024-06-26T15:07:24.4968070 v2 66345 2024-05-09 A novel Arbitrary Lagrangian Eulerian Smooth Particle Hydrodynamics algorithm for nonlinear solid dynamics 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false cecc02ef54af32640274d537577a103e Paulo Refachinho De Campos Paulo Refachinho De Campos true false 97bede20cc14db118af8abfbb687e895 0000-0003-0001-0121 Clare Wood Clare Wood true false 2024-05-09 ACEM This paper introduces a novel Smooth Particle Hydrodynamics (SPH) computational framework that incorporates an Arbitrary Lagrangian Eulerian (ALE) formalism, expressed through a system of first-order conservation laws. In addition to the standard material and spatial configurations, an additional (fixed) referential configuration is introduced. The ALE conservative framework is established based on the fundamental conservation principles, including mass, linear momentum and the first law of thermodynamics represented through entropy density. A key contribution of this work lies in the evaluation of the physical deformation gradient tensor, which measures deformation from material to spatial configuration through a multiplicative decomposition into two auxiliary deformation gradient tensors. Both of the deformation tensors are obtained via additional first-order conservation equations. Interestingly, the new ALE conservative formulation will be shown to degenerate into alternative mixed systems of conservation laws for solid dynamics: particle-shifting, velocity-shifting and Eulerian formulations. The framework also considers path- and/or strain rate-dependent constitutive models, such as isothermal plasticity and thermo-visco-plasticity, by integrating evolution equations for internal state variables. Another contribution of this paper is the evaluation of ALE motion (known as smoothing procedure) by solving a conservation-type momentum equation. This procedure is indeed useful for maintaining a regular particle distribution and enhancing solution accuracy in regions characterised by large plastic flows. The hyperbolicity of the underlying system is ensured and accurate wave speed bounds in the context of ALE description are presented, crucial for ensuring the stability of explicit time integrators. For spatial discretisation, a Godunov-type SPH method is employed and adapted. To guarantee stability from the semi-discretisation standpoint, a carefully designed numerical stabilisation is introduced. The Lyapunov stability analysis is carried out by assessing the time rate of the Ballistic energy of the system, aiming to ensure non-negative entropy production. In order to ensure the global conservation of angular momentum, we employ a three-stage Runge–Kutta time integrator together with a discrete angular momentum projection algorithm. Finally, a range of three dimensional benchmark problems are examined to illustrate the robustness and applicability of the framework. The developed ALE SPH scheme outperforms the Total Lagrangian SPH framework, particularly excelling in capturing plasticity regimes with optimal computational efficiency. Journal Article Computer Methods in Applied Mechanics and Engineering 427 117055 Elsevier BV 0045-7825 Solid dynamics, Conservation laws, Smooth Particle Hydrodynamics, Arbitrary Lagrangian Eulerian, Ballistic, Large strain 1 7 2024 2024-07-01 10.1016/j.cma.2024.117055 COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM Swansea University Another institution paid the OA fee CHL, TJ and SJ acknowledge the support provided by FIFTY2 Technology GmbH via project reference 322835. AJG acknowledges the support provided by UK AWE via project PO 40062030. JB acknowledges the financial support received via project POTENTIAL (PID2022141957OB-C21) funded by MCIN/AEI/10.13039/501100011033/FEDER, UE. 2024-06-26T15:07:24.4968070 2024-05-09T09:47:10.7696313 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering Chun Hean Lee 1 Antonio Gil 0000-0001-7753-1414 2 Paulo Refachinho De Campos 3 Javier Bonet 4 Tadas Jaugielavicius 5 Shreyas Joshi 6 Clare Wood 0000-0003-0001-0121 7 66345__30757__f436dada9f1843caaca2dd609016d94b.pdf 66345.VoR.pdf 2024-06-26T15:06:38.7132868 Output 17743465 application/pdf Version of Record true © 2024 The Author(s). This is an open access article under the CC BY license. true eng http://creativecommons.org/licenses/by/4.0/
title A novel Arbitrary Lagrangian Eulerian Smooth Particle Hydrodynamics algorithm for nonlinear solid dynamics
spellingShingle A novel Arbitrary Lagrangian Eulerian Smooth Particle Hydrodynamics algorithm for nonlinear solid dynamics
Antonio Gil
Paulo Refachinho De Campos
Clare Wood
title_short A novel Arbitrary Lagrangian Eulerian Smooth Particle Hydrodynamics algorithm for nonlinear solid dynamics
title_full A novel Arbitrary Lagrangian Eulerian Smooth Particle Hydrodynamics algorithm for nonlinear solid dynamics
title_fullStr A novel Arbitrary Lagrangian Eulerian Smooth Particle Hydrodynamics algorithm for nonlinear solid dynamics
title_full_unstemmed A novel Arbitrary Lagrangian Eulerian Smooth Particle Hydrodynamics algorithm for nonlinear solid dynamics
title_sort A novel Arbitrary Lagrangian Eulerian Smooth Particle Hydrodynamics algorithm for nonlinear solid dynamics
author_id_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2
cecc02ef54af32640274d537577a103e
97bede20cc14db118af8abfbb687e895
author_id_fullname_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio Gil
cecc02ef54af32640274d537577a103e_***_Paulo Refachinho De Campos
97bede20cc14db118af8abfbb687e895_***_Clare Wood
author Antonio Gil
Paulo Refachinho De Campos
Clare Wood
author2 Chun Hean Lee
Antonio Gil
Paulo Refachinho De Campos
Javier Bonet
Tadas Jaugielavicius
Shreyas Joshi
Clare Wood
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 427
container_start_page 117055
publishDate 2024
institution Swansea University
issn 0045-7825
doi_str_mv 10.1016/j.cma.2024.117055
publisher Elsevier BV
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering
document_store_str 1
active_str 0
description This paper introduces a novel Smooth Particle Hydrodynamics (SPH) computational framework that incorporates an Arbitrary Lagrangian Eulerian (ALE) formalism, expressed through a system of first-order conservation laws. In addition to the standard material and spatial configurations, an additional (fixed) referential configuration is introduced. The ALE conservative framework is established based on the fundamental conservation principles, including mass, linear momentum and the first law of thermodynamics represented through entropy density. A key contribution of this work lies in the evaluation of the physical deformation gradient tensor, which measures deformation from material to spatial configuration through a multiplicative decomposition into two auxiliary deformation gradient tensors. Both of the deformation tensors are obtained via additional first-order conservation equations. Interestingly, the new ALE conservative formulation will be shown to degenerate into alternative mixed systems of conservation laws for solid dynamics: particle-shifting, velocity-shifting and Eulerian formulations. The framework also considers path- and/or strain rate-dependent constitutive models, such as isothermal plasticity and thermo-visco-plasticity, by integrating evolution equations for internal state variables. Another contribution of this paper is the evaluation of ALE motion (known as smoothing procedure) by solving a conservation-type momentum equation. This procedure is indeed useful for maintaining a regular particle distribution and enhancing solution accuracy in regions characterised by large plastic flows. The hyperbolicity of the underlying system is ensured and accurate wave speed bounds in the context of ALE description are presented, crucial for ensuring the stability of explicit time integrators. For spatial discretisation, a Godunov-type SPH method is employed and adapted. To guarantee stability from the semi-discretisation standpoint, a carefully designed numerical stabilisation is introduced. The Lyapunov stability analysis is carried out by assessing the time rate of the Ballistic energy of the system, aiming to ensure non-negative entropy production. In order to ensure the global conservation of angular momentum, we employ a three-stage Runge–Kutta time integrator together with a discrete angular momentum projection algorithm. Finally, a range of three dimensional benchmark problems are examined to illustrate the robustness and applicability of the framework. The developed ALE SPH scheme outperforms the Total Lagrangian SPH framework, particularly excelling in capturing plasticity regimes with optimal computational efficiency.
published_date 2024-07-01T20:30:34Z
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score 11.04748

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