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

作者：Thomas B. J. di Giusto, Chun Hean Lee, Antonio J. Gil, Javier Bonet, Clare Wood, Matteo Giacomini · 发表于：Journal of Computational Physics · 年份：2024 · DOI：10.1016/j.jcp.2024.113322 · 被引用次数：9 · 研究领域：Computational Fluid Dynamics and Aerodynamics、Advanced Numerical Methods in Computational Mathematics、Numerical methods for differential equations

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, ...