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.
翻译:在这项工作中,我们将标准适应网格改进和粗化连接到可缩放的奥氏树底底底底底部,以及强健不适的固定元素配方,以便自动和高效地解决在复杂地貌上出现的大规模非线性固态机械问题,作为标准体装配、无结构网格生成和图形分割战略的替代。我们特别注意那些需要专门处理的方面,以扩展在平行的基于树的可伸缩性树本底部底部的不适宜 h适应性总总元素方法,最近为线性天平伸缩问题开发的阵列,以处理固体机械的非线性问题。为了准确和高效地捕捉在非线性固态机械问题中经常出现的局部非线性非线性固态固态固态机械问题,我们用假时间步制的配方,结合了由外观误差估计器驱动的 h-适应性动态网格生成和平流体分隔法的精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度精度