Rapid Voxel-Based Digital-Computation for Complex Microstructured Media

A technique based on voxel (3D “volume pixels”) representation of microstructures and corresponding digital solution methods is developed for representative volume element type calculations, which avoids computationally expensive steps involved in usual Finite Element procedures such as topologically conforming meshing, mapping, volume integration, stiffness matrix generation and matrix-based solution methods. The process proceeds by converting the material microstructure into voxels. The problem then becomes “digital” on a regular “voxel-grid”, directly manipulating voxel values, allowing extremely fast methods to be used to construct derivatives and the solve the system. In this paper, we illustrate the process of voxelization, derivative construction and solution, and also supply an analysis of the operation counts. Numerical examples are provided to illustrate the approach.