A tool for design of heterogeneous materials with desired physical properties using statistical continuum theory

Abstract

A new efficient and simple algorithm based on two-point probability functions was developed to construct isotropic and anisotropic heterogeneous microstructures with desired effective physical property. To take into account the complex heterogeneities geometry, the developed microstructure design tool uses the strong-contrast formulations of the statistical continuum theory to compute the effective properties. This approach uses n-point correlation functions to take into account the details of the microstructure. The microstructure construction starts by randomly distributing unit-cells that represent heterogeneities within the matrix. These initial unit-cells are represented by one pixel each that grows to become multi-pixel heterogeneities using an optimization algorithm. The construction is achieved by minimizing an objective function (OF) defined as the difference between the effective desired property and the one calculated at each iteration. As an application, the developed optimization algorithm is used to construct isotropic and anisotropic porous materials with desired effective thermal conductivity. The developed algorithm can be used as a tool to aid in heterogeneous materials design and also for understanding the links between the microstructure and the material properties.