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A first-order hyperbolic Arbitrary Lagrangian Eulerian conservation formulation for non-linear solid dynamics
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Chun Hean Lee,
Javier Bonet,
Matteo Giacomini
International Journal for Numerical Methods in Engineering, Volume: 125, Issue: 15
Swansea University Authors:
Thomas Di Giusto, Antonio Gil
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DOI (Published version): 10.1002/nme.7467
Abstract
The paper introduces a computational framework using a novel Arbitrary Lagrangian Eulerian (ALE) formalism in the form of a system of first-order conservation laws. In addition to the usual material and spatial configurations, an additional referential (intrinsic) configuration is introduced in orde...
| Published in: | International Journal for Numerical Methods in Engineering |
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| ISSN: | 0029-5981 1097-0207 |
| Published: |
Wiley
2024
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa65812 |
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| Abstract: |
The paper introduces a computational framework using a novel Arbitrary Lagrangian Eulerian (ALE) formalism in the form of a system of first-order conservation laws. In addition to the usual material and spatial configurations, an additional referential (intrinsic) configuration is introduced in order to disassociate material particles from mesh positions. Using isothermal hyperelasticity as a starting point, mass, linear momentum and total energy conservation equations are written and solved with respect to the reference configuration. In addition, with the purpose of guaranteeing equal order of convergence of strains/stresses and velocities/displacements, the computation of the standard deformation gradient tensor (measured from material to spatial configuration) is obtained via its multiplicative decomposition into two auxiliary deformation gradient tensors, both computed via additional first-order conservation laws. Crucially, the new ALE conservative formulation will be shown to degenerate elegantly into alternative mixed systems of conservation laws such as Total Lagrangian, Eulerian and Updated Reference Lagrangian. Hyperbolicity of the system of conservation laws will be shown and the accurate wave speed bounds will be presented, the latter critical to ensure stability of explicit time integrators. For spatial discretisation, a vertex-based Finite Volume method is employed and suitably adapted. To guarantee stability from both the continuum and the semi-discretisation standpoints, an appropriate numerical interface flux (by means of the Rankine–Hugoniot jump conditions) is carefully designed and presented. Stability is demonstratedvia the use of the time variation of the Hamiltonian of the system, seeking to ensure the positiveproduction of numerical entropy. A range of three dimensional benchmark problems will be presented in order to demonstrate the robustness and reliability of the framework. Examples will be restricted to the case of isothermal reversible elasticity to demonstrate the potential of the new formulation. |
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| Keywords: |
Arbitrary Lagrangian Eulerian, conservation laws, fast dynamics, Hamiltonian, large strain, finite volume method |
| College: |
Faculty of Science and Engineering |
| Funders: |
European Union Horizon 2020. Grant Number: 764636;
EPSRC. Grant Number: EP/R008531/1;
K AWE. Grant Number: PO 40062030;
MCIN. Grant Numbers: PID2020-113463RB-C33, PID2022-141957OB-C21, CEX2018-000797-S |
| Issue: |
15 |