A novel Arbitrary Lagrangian Eulerian formulation for a system of first order conservation laws in fast solid dynamics

This work introduces a new Arbitrary Lagrangian Eulerian mixed formulation based on a hyperbolic system of first order conservation laws. A multiplicative decomposition of the natural deformation is performed and the resulting components, the material and spatial deformation gradients, abide by their own conservation laws. The material motion, accounting for the deformation of the mesh, is obtained from a conservation law based on a smoothing potential in which the magnitude is controlled by an user-defined parameter. This new ALE formulation degenerates in Total Lagrangian or Eulerian formulations, and therefore aims at bridging the gap between Computational Solid and Fluid Dynamics communities. An edge-based vertex-centred finite volume method is used to numerically assess this new formulation implemented into the open source software OpenFOAM. This methodology will be tested on fast transient solid dynamics problems based on large deformations, circumventing some of the difficulties often encountered in displacement-based formulations.