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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
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-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.
Keywords: Total Lagrangian; SPH; Finite strain structural dynamics; Completeness; Complete Riemann term
College: Faculty of Science and Engineering
Funders: 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.
Issue: 1
Start Page: 147
End Page: 179

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