Fast Reconstruction of Microstructures with Ellipsoidal Inclusions Using Analytical Descriptors

Microstructure reconstruction is an important and emerging aspect of computational materials engineering and multiscale modeling and simulation. Despite extensive research and fast progress in the field, the application of descriptor-based reconstruction remains limited by computational resources. Common methods for increasing the computational feasibility of descriptor-based microstructure reconstruction lie in approximating the microstructure by simple geometrical shapes and by utilizing differentiable descriptors to enable gradient-based optimization. The present work combines these two ideas for structures composed of non-overlapping ellipsoidal inclusions such as magnetorheological elastomers. This requires to express the descriptors as a function of the microstructure parametrization. Deriving these relations leads to analytical solutions that further speed up the reconstruction procedure. Based on these descriptors, microstructure reconstruction is formulated as a multi-stage optimization procedure. The developed algorithm is validated by means of different numerical experiments and advantages and limitations are discussed in detail.