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

TL;DR

This paper introduces a robust, scalable unfitted adaptive finite element framework for nonlinear solid mechanics, capable of handling complex geometries and large-scale problems efficiently on parallel supercomputers.

Contribution

It extends unfitted h-adaptive finite element methods to nonlinear solid mechanics, enabling efficient, accurate simulations on complex geometries with parallel scalability.

Findings

Successfully modeled inelastic behavior of various materials.

Achieved solution of large problems with up to 11.7 million DOFs in under two hours.

Validated the method with benchmark and complex geometry problems.

Abstract

In this work, we bridge standard adaptive mesh refinement and coarsening on scalable octree background meshes and robust unfitted finite element formulations for the automatic and efficient solution of large-scale nonlinear solid mechanics problems posed on complex geometries, as an alternative to standard body-fitted formulations, unstructured mesh generation and graph partitioning strategies. We pay special attention to those aspects requiring a specialized treatment in the extension of the unfitted h-adaptive aggregated finite element method on parallel tree-based adaptive meshes, recently developed for linear scalar elliptic problems, to handle nonlinear problems in solid mechanics. In order to accurately and efficiently capture localized phenomena that frequently occur in nonlinear solid mechanics problems, we perform pseudo time-stepping in combination with h-adaptive dynamic mesh refinement and rebalancing 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 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 hollows distributed in a Simple Cubic array. This test involves a discrete domain with up to 11.7M Degrees Of Freedom solved in less than two hours on 3072 cores of a parallel supercomputer.