Automatic parallel generation of finite element meshes for complex spatial structures

摘要

Recent developments in experimental techniques are enabling researchers to non-destructively characterize complex spatial structures with multiple constituents, e.g. polycrystalline aggregates. However, a combination of the high level of detail of the experimental data and often extreme geometry complexity make the building of models of such structures highly difficult and demanding. Finite element (FE) pre-processor tools can often be inadequate, especially when the structure contains multiple constituents and when the model building process has to be automatized. This paper proposes a novel framework for automatic and parallelized generation of FE models from discrete spatial data (voxels) procured from experimental techniques, e.g. 3D X-ray diffraction microscopy or X-ray diffraction contrast tomography (DCT). The technique can also be applied to analytical spatial geometries. The framework consists of reconstructing the surfaces of different constituents from the experimental data, generating FE meshes of these surfaces, followed by volume meshing of the constituents interior while enforcing the already generated surfaces meshes. This approach assures a conformal mesh between the adjoining surfaces and at the same time enables a fully independent and parallel meshing of the constituents. The conformal mesh allows for a variety of connectivity models between the constituents, including layers of cohesive elements for simulating the grain boundaries. The applicability of the approach is demonstrated first by creating a FE model of a 400 μm diameter stainless steel wire characterized in 3D by DCT. FE model generation of spatial Voronoi tessellations, representing models of polycrystalline aggregates with up to 5000 grains, is then demonstrated. Here, anisotropic elasticity and crystal plasticity constitutive laws are used to estimate the scatter of the macroscopic responses due the random nature of the grains' crystallographic orientations. At 2000 grains this influence is shown to be very small.