Algorithms for automated meshing and unit cell analysis of periodic composites with hierarchical tri-quadratic tetrahedral elements

Abstract

Unit cell homogenization techniques together with the finite element method are very effective for computing equivalent mechanical properties of composites and heterogeneous materials systems. For systems with very complicated material arrangements, traditional, manual mesh generation can be a considerable obstacle to usage of these techniques. This problem is addressed here by developing automated meshing techniques that start from a hierarchical quad-tree (in 2D) or oc-tree (in 3D) mesh of pixel or voxel elements. From the pixel/voxel mesh, algorithms are presented for successive element splitting and nodal shifting to arrive at final meshes that accurately capture both material arrangements and constituent volume fractions, and the material-scale stress and strain fields within the composite under different modalities of loading. The performance and associated convergence behaviour of the proposed techniques are demonstrated on both densely packed fibre and particulate composites, and on 3D textile-reinforced composites. © 2003 John Wiley and Sons, Ltd.