Micrmechanicalmodeling of ceramics-based composites via voronoi-delaunay networks

This article examines the mechanical behavior of a 2D class of random media using a discrete modeling approach. To capture physical randomness, the paper utilizes the Voronoi tessellation to simulate a random microstructure of a two-phase ceramics-based composite. Given the duality of the Delaunay triangulation to the Voronoi tessellation, the presented work studies the effect of randomness in this microstructure upon the effective elastic moduli. Interactions between neighboring grains are modeled via the Delaunay network in which each vertex represents a grain and each edge is a two-force member acting as a linear spring. More precisely, we consider finite ―windows of observations as a statistical planar element (SPE). A proper displacement-controlled (essential) boundary condition applied to the SPE generates approximate uniform strain field in the models, which corresponds to calculating one elastic modulus at a time. Then, the effective Young's modulus and Poisson's ratio of the continuum are extracted from the calculated elastic moduli. Conducting a number of Monte Carlo simulations for different parameter setups allows estimating the first and second order characteristic of the random fields of effective elastic moduli. The results obtained support the usefulness of this framework for developing analytical models of various random heterogeneous solids.