A robust and scalable unfitted adaptive finite element framework for nonlinear solid mechanics.

We extend the unfitted $h$-adaptive Finite Element Method ($h$-AgFEM) on parallel tree-based adaptive meshes, recently developed for linear scalar elliptic problems, to handle nonlinear problems in solid mechanics. Leveraging $h$-AgFEM on locally-adapted, non-conforming, tree-based meshes, and its parallel distributed-memory implementation, we can tackle large-, multi-scale problems posed on complex geometries. On top of that, in order to accurately and efficiently capture localized phenomena that frequently occur in nonlinear solid mechanics problems, we propose an algorithm to perform pseudo time-stepping in combination with $h$-adaptive dynamic mesh refinement and re-balancing driven by a-posteriori error estimators. The method is implemented considering both irreducible and mixed (u/p) formulations and thus it is able to robustly face problems involving incompressible materials. In the numerical experiments, both formulations are used to model the inelastic behavior of a wide range of compressible and incompressible materials. First, a selected set of state-of-the-art benchmarks are reproduced as a verification step. Second, a set of experiments is presented with problems involving complex geometries. Among them, we model a cantilever beam problem with spherical voids whose distribution is based on a Cube Closest Packing (CCP). This test involves a discrete domain with up to 11.7M Degrees Of Freedom (DOFs) solved in less than two hours on 3072 cores of a parallel supercomputer.