Adaptive octree-based finite element analysis of two- and three-dimensional indentation problems

摘要

In recent years, much has been done to develop numerical tools to study the three-dimensional nature of the Earth's lithosphere deformation. DOUAR is one of them: it is a new ALE Finite Element code that is based on an adaptive grid, a key feature in the capture of localized deformation. In order to illustrate this, various simulations of punch experiments have been performed on rigid plastic materials with von Mises and Drucker-Prager type of rheologies. We present the grid refinement algorithm based on strain rate measurements and rederive the plane strain punch analytical solution which allows us to test the accuracy of our results. Various 3-D strip punches experiments with different aspect ratios show DOUAR's ability to capture complex fault patterns. We also discuss the degree to which the incompressibility and rigid plasticity constraints are satisfied. Finally, we show the results of a crustal-scale deformation experiment demonstrating the potential of the octree-based mesh refinement algorithm to solve complex three-dimensional geodynamical problems with great efficiency and accuracy.