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An enhanced total Lagrangian SPH for non-linear and finite strain elastic structural dynamics

Takafumi Gotoh, Daiki Sakoda, Abbas Khayyer, Chun Hean Lee, Antonio Gil Orcid Logo, Hitoshi Gotoh, Javier Bonet

Computational Mechanics, Volume: 76, Issue: 1, Pages: 147 - 179

Swansea University Author: Antonio Gil Orcid Logo

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DOI (Published version): 10.1007/s00466-024-02592-z

Abstract

The paper presents a variationally consistent Total Lagrangian SPH (TLSPH) model for non-linear and finite strain elastic structural dynamics. To enhance the approximation of stresses (dynamics) and thus accelerations (kinematics), the deformation gradient computation is enhanced to ensure second-or...

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Published in: Computational Mechanics
ISSN: 0178-7675 1432-0924
Published: Springer Nature 2025
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URI: https://cronfa.swan.ac.uk/Record/cronfa68680
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last_indexed 2025-10-01T10:04:33Z
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spelling 2025-09-30T14:38:04.1171700 v2 68680 2025-01-13 An enhanced total Lagrangian SPH for non-linear and finite strain elastic structural dynamics 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2025-01-13 ACEM The paper presents a variationally consistent Total Lagrangian SPH (TLSPH) model for non-linear and finite strain elastic structural dynamics. To enhance the approximation of stresses (dynamics) and thus accelerations (kinematics), the deformation gradient computation is enhanced to ensure second-order completeness and accordingly the discretized momentum equation is also reformulated so that the accelerations are consistently obtained with respect to the targeted second-order completeness. In addition, a novel Riemann stabilization term is proposed with respect to the rank deficiency of TLSPH particularly for challenging structural dynamics problems including fast dynamics and kinematical discontinuities. The new Riemann term is second-order accurate in space and includes a limiter for effective stabilization. This stabilization term is derived from the material acoustic tensor of the solid model employed, carefully accounting for both volumetric (compression) and shear wave contributions. The proposed TLSPH including the C2nd (2nd-order Completeness) and cR (complete Riemann term including volumetric and shear wave contributions) schemes is verified by considering six classical benchmark tests. Journal Article Computational Mechanics 76 1 147 179 Springer Nature 0178-7675 1432-0924 Total Lagrangian; SPH; Finite strain structural dynamics; Completeness; Complete Riemann term 1 7 2025 2025-07-01 10.1007/s00466-024-02592-z COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM Swansea University Not Required This study is supported by JSPS (Japan Society for the Promotion of Science) Grant No. 24K07680. The first author appreciates the JST (Japan Science and Technology Agency) SPRING Grant No. JPMJSP2110. 2025-09-30T14:38:04.1171700 2025-01-13T12:41:59.0525791 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering Takafumi Gotoh 1 Daiki Sakoda 2 Abbas Khayyer 3 Chun Hean Lee 4 Antonio Gil 0000-0001-7753-1414 5 Hitoshi Gotoh 6 Javier Bonet 7 68680__33291__2c81dcc789774a5ca038d0ad1865ecd4.pdf 68680.pdf 2025-01-13T12:47:22.5043941 Output 21061160 application/pdf Accepted Manuscript true Author accepted manuscript document released under the terms of a Creative Commons CC-BY licence using the Swansea University Research Publications Policy (rights retention). true eng https://creativecommons.org/licenses/by/4.0/deed.en
title An enhanced total Lagrangian SPH for non-linear and finite strain elastic structural dynamics
spellingShingle An enhanced total Lagrangian SPH for non-linear and finite strain elastic structural dynamics
Antonio Gil
title_short An enhanced total Lagrangian SPH for non-linear and finite strain elastic structural dynamics
title_full An enhanced total Lagrangian SPH for non-linear and finite strain elastic structural dynamics
title_fullStr An enhanced total Lagrangian SPH for non-linear and finite strain elastic structural dynamics
title_full_unstemmed An enhanced total Lagrangian SPH for non-linear and finite strain elastic structural dynamics
title_sort An enhanced total Lagrangian SPH for non-linear and finite strain elastic structural dynamics
author_id_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2
author_id_fullname_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio Gil
author Antonio Gil
author2 Takafumi Gotoh
Daiki Sakoda
Abbas Khayyer
Chun Hean Lee
Antonio Gil
Hitoshi Gotoh
Javier Bonet
format Journal article
container_title Computational Mechanics
container_volume 76
container_issue 1
container_start_page 147
publishDate 2025
institution Swansea University
issn 0178-7675
1432-0924
doi_str_mv 10.1007/s00466-024-02592-z
publisher Springer Nature
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 The paper presents a variationally consistent Total Lagrangian SPH (TLSPH) model for non-linear and finite strain elastic structural dynamics. To enhance the approximation of stresses (dynamics) and thus accelerations (kinematics), the deformation gradient computation is enhanced to ensure second-order completeness and accordingly the discretized momentum equation is also reformulated so that the accelerations are consistently obtained with respect to the targeted second-order completeness. In addition, a novel Riemann stabilization term is proposed with respect to the rank deficiency of TLSPH particularly for challenging structural dynamics problems including fast dynamics and kinematical discontinuities. The new Riemann term is second-order accurate in space and includes a limiter for effective stabilization. This stabilization term is derived from the material acoustic tensor of the solid model employed, carefully accounting for both volumetric (compression) and shear wave contributions. The proposed TLSPH including the C2nd (2nd-order Completeness) and cR (complete Riemann term including volumetric and shear wave contributions) schemes is verified by considering six classical benchmark tests.
published_date 2025-07-01T05:26:08Z
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