Di Giusto, Thomas B.J. and Lee, Chun Hean and Gil, A.J. and Bonet, Javier and Giacomini, Matteo (2024) A first-order hyperbolic arbitrary Lagrangian Eulerian conservation formulation for non-linear solid dynamics. International Journal for Numerical Methods in Engineering, 125 (15): e7467. ISSN 0029-5981
AI Summary:
The paper introduces a computational framework using a novel Arbitrary Lagrangian Eulerian ALE formalism. The framework is designed to ensure stability and accuracy in the simulation of complex physical phenomena.AI Topics:
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 demonstrated via the use of the time variation of the Hamiltonian of the system, seeking to ensure the positive production 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.
Di Giusto, Thomas B.J.
Author
Di Giusto, Thomas B.J. and Lee, Chun Hean and Gil, Antonio J. and Bonet, Javier and Wood, Clare and Giacomini, Matteo (2024) A first-order hyperbolic Arbitrary Lagrangian Eulerian conservation formulation for nonlinear solid dynamics in irreversible processes. Journal of Computational Physics, 518: 113322. ISSN 0021-9991
Di Giusto, Thomas B.J. and Lee, Chun Hean and Gil, A.J. and Bonet, Javier and Giacomini, Matteo (2024) A first-order hyperbolic arbitrary Lagrangian Eulerian conservation formulation for non-linear solid dynamics. International Journal for Numerical Methods in Engineering, 125 (15): e7467. ISSN 0029-5981
See full publications listLee, Chun Hean
Author
Di Giusto, Thomas B.J. and Lee, Chun Hean and Gil, Antonio J. and Bonet, Javier and Wood, Clare and Giacomini, Matteo (2024) A first-order hyperbolic Arbitrary Lagrangian Eulerian conservation formulation for nonlinear solid dynamics in irreversible processes. Journal of Computational Physics, 518: 113322. ISSN 0021-9991
Khayyer, Abbas and Lee, Chun Hean (2024) Discussion on “comparative study on volume conservation among various SPH models for flows of different levels of violence, coastal engineering, volume 191, August 2024, 104 521” by Wang et al. Coastal Engineering, 192: 104565. ISSN 0378-3839
Di Giusto, Thomas B.J. and Lee, Chun Hean and Gil, A.J. and Bonet, Javier and Giacomini, Matteo (2024) A first-order hyperbolic arbitrary Lagrangian Eulerian conservation formulation for non-linear solid dynamics. International Journal for Numerical Methods in Engineering, 125 (15): e7467. ISSN 0029-5981
See full publications listGil, A.J.
Author
Di Giusto, Thomas B.J. and Lee, Chun Hean and Gil, A.J. and Bonet, Javier and Giacomini, Matteo (2024) A first-order hyperbolic arbitrary Lagrangian Eulerian conservation formulation for non-linear solid dynamics. International Journal for Numerical Methods in Engineering, 125 (15): e7467. ISSN 0029-5981
See full publications listBonet, Javier
Author
Di Giusto, Thomas B.J. and Lee, Chun Hean and Gil, Antonio J. and Bonet, Javier and Wood, Clare and Giacomini, Matteo (2024) A first-order hyperbolic Arbitrary Lagrangian Eulerian conservation formulation for nonlinear solid dynamics in irreversible processes. Journal of Computational Physics, 518: 113322. ISSN 0021-9991
Di Giusto, Thomas B.J. and Lee, Chun Hean and Gil, A.J. and Bonet, Javier and Giacomini, Matteo (2024) A first-order hyperbolic arbitrary Lagrangian Eulerian conservation formulation for non-linear solid dynamics. International Journal for Numerical Methods in Engineering, 125 (15): e7467. ISSN 0029-5981
Lee, Chun Hean and Gil, Antonio J. and Refachinho de Campos, Paulo R. and Bonet, Javier and Jaugielavicius, Tadas and Joshi, Shreyas and Wood, Clare (2024) A novel Arbitrary Lagrangian Eulerian Smooth Particle Hydrodynamics algorithm for nonlinear solid dynamics. Computer Methods in Applied Mechanics and Engineering, 427: 117055. ISSN 0045-7825
See full publications listGiacomini, Matteo
Author
Di Giusto, Thomas B.J. and Lee, Chun Hean and Gil, Antonio J. and Bonet, Javier and Wood, Clare and Giacomini, Matteo (2024) A first-order hyperbolic Arbitrary Lagrangian Eulerian conservation formulation for nonlinear solid dynamics in irreversible processes. Journal of Computational Physics, 518: 113322. ISSN 0021-9991
Di Giusto, Thomas B.J. and Lee, Chun Hean and Gil, A.J. and Bonet, Javier and Giacomini, Matteo (2024) A first-order hyperbolic arbitrary Lagrangian Eulerian conservation formulation for non-linear solid dynamics. International Journal for Numerical Methods in Engineering, 125 (15): e7467. ISSN 0029-5981
Lee, Chun Hean and Refachinho de Campos, Paulo R. and Gil, Antonio J. and Giacomini, Matteo and Bonet, Javier (2023) An entropy-stable updated reference Lagrangian smoothed particle hydrodynamics algorithm for thermo-elasticity and thermo-visco-plasticity. Computational Particle Mechanics, 10. pp. 1493-1531. ISSN 2196-4378
See full publications listAvailable under License Creative Commons Attribution.
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