Genetic design of solids possessing a random-particulate microstructure

There exists a variety of difficulties in the computational design of macroscopic solid material properties formed by doping a homogeneous base matrix material with randomly distributed particles having different properties. Three primary problems are (1) the wide array of free microdesign variables, such as particle topology, property phase contrasts and volume fraction, which render the associated objective functions to be highly non-convex; (2) that the associated objective functions are not differentiable with respect to design variables, primarily due to prescribed constraints, such as prespecified restrictions on the microscale stress-field behaviour; and (3) the effective responses of various finite-sized samples, of equal volume but of different random particle distributions, exhibit mutual fluctuations, leading to amplified noise in optimization strategies where objective function sensitivities or comparisons are needed. The focus of this paper is the development of a statistical genetic algorithm which can handle difficulties due to non-convexity, lack of regularity and size effects. Theoretical properties of the overall approach are investigated. Semi-analytical and large-scale numerical examples, involving finite-element type discretizations, are given to illustrate its practical application.