Optimal polyhedral description of 3D polycrystals: Method and application to statistical and synchrotron X-ray diffraction data

A methodology is presented for optimal polyhedral description of 3D polycrystals from experimental properties. This is achieved by determining, by optimization, appropriate attributes of the seeds of Laguerre tessellations. The resulting tessellations are optimal in the sense that no further improvements are possible using convex geometries. The optimization of Laguerre tessellation combines a new, computationally-efficient algorithm for updating tessellations between iterations to a generic optimization algorithm. The method is applied to different types of experimental data, either statistical, such as grain size distributions, or grain-based, as provided by synchrotron X-ray diffraction experiments. It is then shown how the tessellations can be meshed for finite-element simulations. The new method opens the way to more systematic and quantitative analyses of microstructural effects on properties. The presented algorithms are implemented and distributed in the free (open-source) software package Neper.