New algorithms for virtual reconstruction of heterogeneous microstructures

A new set of algorithms is introduced for the virtual reconstruction of heterogeneous material microstructures, in which morphologies of embedded particles/fibers are explicitly represented. As a pre-processing phase, a shape library containing morphologies of heterogeneities, parameterized in terms of Non-Uniform Rational B-Splines (NURBS), is extracted from digital data such as micro-computed tomography images. Two packing algorithms are then introduced to reconstruct an initial (raw) periodic microstructure: In the first approach, a set of hierarchical bounding boxes approximating particle shapes are employed to check for overlap. The second approach, which is specialized for fibrous microstructures, uses the NURBS representation of fiber centerlines during the packing process. An optimization phase is applied to build the final microstructural model, relying either on the Genetic Algorithm to selectively eliminate some of the inclusions or their sequential relocation within the raw microstructure. The objective functions of this optimization phase are designed to replicate the target statistical microstructural descriptors such as the volume fraction, size distribution, and spatial arrangement of inclusions. Several example problems are presented to show the application of these algorithms for synthesizing various heterogeneous microstructures, as well as their finite element modeling and simulation.