A 3D cell-centered ADER MOOD Finite Volume method for solving updated Lagrangian hyperelasticity on unstructured grids

In this paper, we present a conservative cell-centered Lagrangian Finite Volume scheme for solving the hyperelasticity equations on unstructured multidimensional grids. The starting point of approach is FV discretization named EUCCLHYD and introduced in context hydrodynamics. Here, it combined with posteriori Multidimensional Optimal Order Detection (MOOD) limiting strategy to ensure robustness stability at shock waves piecewise linear spatial reconstruction. ADER (Arbitrary high order schemes using DERivatives) adopted obtain second-order accuracy time. This has been successfully tested hydrodynamics work aims extending case hyperelasticity. are written updated framework dedicated numerical derived terms nodal solver, Geometrical Conservation Law (GCL) compliance, subcell forces compatible discretization. method implemented 3D under MPI parallelization allowing handle genuinely large meshes. A relatively set test cases presented assess ability achieve effective second smooth flows, maintaining an essentially non-oscillatory behavior general across discontinuities ensuring least physical admissibility solution where appropriate. Pure elastic neo-Hookean non-linear materials considered our benchmark problems 2D 3D. These feature material bending, impact, compression, deformation further bouncing/detaching motions.