Computing property variability of polycrystals induced by grain size and orientation uncertainties

Multiscale computational methods that link microscale models to macro-properties have practical significance. It is difficult to obtain probability distribution functions (PDFs) that provide a complete representation of microstructural variability in three-dimensional polycrystalline materials using limited information since this inverse problem is highly ill-posed. We use the maximum entropy (MaxEnt) principle to compute a PDF of microstructures based on given information about a microstructural system. Microstructural features are incorporated into the maximum entropy framework using data obtained from experiments or simulations. Microstructures are sampled from the computed MaxEnt PDF using concepts from computational geometry and Voronoi cell tessellations. These microstructures are then interrogated in virtual deformation tests, and by using homogenization techniques the variability of non-linear macro-properties is computed.