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
AI Summary:
This paper introduces a novel Smooth Particle Hydrodynamics (SPH) computational framework that incorporates an Arbitrary Lagrangian Eulerian (ALE) formalism. The framework is designed to simulate complex fluid dynamics and solid mechanics problems, particularly those involving large deformations and plasticity.AI Topics:
This paper introduces a novel Smooth Particle Hydrodynamics (SPH) computational framework that incorporates an Arbitrary Lagrangian Eulerian (ALE) formalism, expressed through a system of first-order conservation laws. In addition to the standard material and spatial configurations, an additional (fixed) referential configuration is introduced. The ALE conservative framework is established based on the fundamental conservation principles, including mass, linear momentum and the first law of thermodynamics represented through entropy density. A key contribution of this work lies in the evaluation of the physical deformation gradient tensor, which measures deformation from material to spatial configuration through a multiplicative decomposition into two auxiliary deformation gradient tensors. Both of the deformation tensors are obtained via additional first-order conservation equations. Interestingly, the new ALE conservative formulation will be shown to degenerate into alternative mixed systems of conservation laws for solid dynamics: particle-shifting, velocity-shifting and Eulerian formulations. The framework also considers path- and/or strain rate-dependent constitutive models, such as isothermal plasticity and thermo-visco-plasticity, by integrating evolution equations for internal state variables. Another contribution of this paper is the evaluation of ALE motion (known as smoothing procedure) by solving a conservation-type momentum equation. This procedure is indeed useful for maintaining a regular particle distribution and enhancing solution accuracy in regions characterised by large plastic flows. The hyperbolicity of the underlying system is ensured and accurate wave speed bounds in the context of ALE description are presented, crucial for ensuring the stability of explicit time integrators. For spatial discretisation, a Godunov-type SPH method is employed and adapted. To guarantee stability from the semi-discretisation standpoint, a carefully designed numerical stabilisation is introduced. The Lyapunov stability analysis is carried out by assessing the time rate of the Ballistic energy of the system, aiming to ensure non-negative entropy production. In order to ensure the global conservation of angular momentum, we employ a three-stage Runge–Kutta time integrator together with a discrete angular momentum projection algorithm. Finally, a range of three dimensional benchmark problems are examined to illustrate the robustness and applicability of the framework. The developed ALE SPH scheme outperforms the Total Lagrangian SPH framework, particularly excelling in capturing plasticity regimes with optimal computational efficiency.
Lee, 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, Antonio 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
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
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 listRefachinho de Campos, Paulo R.
Author
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
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 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 listJaugielavicius, Tadas
Author
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 listJoshi, Shreyas
Author
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 listWood, Clare
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
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 listAvailable under License Creative Commons Attribution.
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