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A first-order hyperbolic Arbitrary Lagrangian Eulerian conservation formulation for nonlinear solid dynamics in irreversible processes

Thomas Di Giusto, Chun Hean Lee, Antonio Gil Orcid Logo, Javier Bonet, Clare Wood Orcid Logo, Matteo Giacomini

Journal of Computational Physics, Volume: 518, Start page: 113322

Swansea University Authors: Thomas Di Giusto, Antonio Gil Orcid Logo, Clare Wood Orcid Logo

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DOI (Published version): 10.1016/j.jcp.2024.113322

Abstract

The paper introduces a computational framework that makes use of a novel Arbitrary Lagrangian Eulerian (ALE) conservation law formulation for nonlinear solid dynamics. In addition to the standard mass conservation law and the linear momentum conservation law, the framework extends its application to...

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Published in: Journal of Computational Physics
ISSN: 0021-9991
Published: Elsevier BV 2024
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URI: https://cronfa.swan.ac.uk/Record/cronfa67331
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Abstract: The paper introduces a computational framework that makes use of a novel Arbitrary Lagrangian Eulerian (ALE) conservation law formulation for nonlinear solid dynamics. In addition to the standard mass conservation law and the linear momentum conservation law, the framework extends its application to consider more general irreversible processes such as thermo-elasticity and thermo-visco-plasticity. This requires the incorporation of the first law of thermodynamics, expressed in terms of the entropy density, as an additional conservation law. To disassociate material particles from mesh positions, the framework introduces an additional reference configuration, extending beyond conventional material and spatial descriptions. The determination of the mesh motion involves the solution of a conservation-type momentum equation, ensuring optimal mesh movement and contributing to maintaining a high-quality mesh and improving solution accuracy, particularly in regions undergoing large plastic flows. To maintain equal convergence orders for all variables (strains/stresses, velocities/displacements and temperature/entropy), the standard deformation gradient tensor (measured from material to spatial configuration) is evaluated through a multiplicative decomposition into two auxiliary deformation gradient tensors. Both are obtained through additional first-order conservation laws. The exploitation of the hyperbolic nature of the underlying system, together with accurate wave speed bounds, ensures the stability of explicit time integrators. For spatial discretisation, a vertex-centred Godunov-type Finite Volume method is employed and suitably adapted to the formulation at hand. To guarantee stability from both the continuum and the semi-discretisation standpoints, a carefully designed numerical interface flux is presented. Lyapunov stability analysis is carried out by evaluating the time variation of the Ballistic energy of the system, aiming to ensure the positive production of numerical entropy. Finally, a variety of three dimensional benchmark problems are presented to illustrate the robustness and applicability of the framework.
Keywords: Solid dynamics; Conservation laws; Arbitrary Lagrangian Eulerian; Ballistic; Large strain; Godunov-type finite volume method
College: Faculty of Science and Engineering
Funders: The first, second and third authors would like to acknowledge the financial support received through the project Marie Skłodowska-Curie ITN-EJD ProTechTion, funded by the European Union Horizon 2020 research and innovation program with grant number 764636. CHL acknowledges 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 (PID2022-141957OB-C21) funded by MICIU/AEI/10.13039/501100011033/FEDER, UE. MG acknowledges the Spanish Ministry of Science, Innovation and Universities and Spanish State Research Agency MICIU/AEI/10.13039/501100011033 (Grants No. PID2020-113463RB-C33 and CEX2018-000797-S) and the Generalitat de Catalunya (Grant No. 2021-SGR-01049). MG is Fellow of the Serra Húnter Programme of the Generalitat de Catalunya.
Start Page: 113322

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