Multi-scale computational homogenization of composites with voxel-based meshing and element splitting techniques

Unit cell homogenization techniques are frequently used with the finite element method to compute effective mechanical properties for a wide range of different composites and their associated material structures. But, there are two basic characteristics that distinguish unit cell meshing from that of other mechanical systems: (1) the displacement periodicity between adjoining unit-cells; and (2) meshing both sides of interior material interfaces. In this dissertation, pixel- (2D) and voxel- (3D) based meshing concepts borrowed from image processing are thus developed and employed to construct the finite element mesh for unit cell model. The potential advantage of these techniques is that generation of unit cell models can be automated, thus requiring far less human time than traditional methods. While voxel-based meshing techniques have many positive attributes, they can be somewhat slow to converge to actual material property characteristics since the mesh boundary does not conform to material interfaces. To address this issue, a hybrid meshing technique that begins with voxel-based mesh and then shifts to conforming techniques that split elements and move nodes to arrive at final meshes. The performance and associated convergence behavior of the proposed voxel- and hybrid-meshing techniques are demonstrated.; Computational unit cell homogenization equipped with the newly developed hybrid mesh generators using element splitting techniques is then applied to analysis of structural systems fabricated with textile composites. Such systems have multiple levels of material structure at different length scales, which makes them hierarchical materials systems. When the length scale associated with variations of macroscopic deformation on one scale is much larger than the unit cell dimensions associated with lower level material structure on a finer scale, then the heterogeneous medium of the finer scale can be appropriately modeled using the effective medium approximation. Herein, unit-cell analysis is utilized to investigate potential analytical forms of hyperelastic effective medium constitutive model for homogenized yarn composites and a reasonable transversely isotropic hyperelastic form of a constitutive model for aligned-fiber composites is obtained based on unit-cell analysis at finite deformations. Then, the model with appropriate material parameters is utilized in textile unit-cell models to calculate potential finite deformation characteristics.