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Algorithms for automated meshing and unit cell analysis of periodic composites with hierarchical tri‐quadratic tetrahedral elements
Author(s) -
Kim Hyung Joo,
Swan Colby C.
Publication year - 2003
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.828
Subject(s) - homogenization (climate) , finite element method , polygon mesh , orthotropic material , mesh generation , computer science , quadratic equation , tetrahedron , voxel , algorithm , computational science , materials science , structural engineering , composite material , mathematics , geometry , engineering , artificial intelligence , computer graphics (images) , biodiversity , ecology , biology
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. Copyright © 2003 John Wiley Sons, Ltd.