Topological design of microstructures of multi-phase materials for maximum stiffness or thermal conductivity

This paper introduces an alternative approach for the topological design of microstructures of materials that are composed of three or more constituent phases. It is assumed that the materials are made up of periodic microstructures. Bi-directional Evolutionary Structural Optimization (BESO) methodology is applied for designing materials' microstructures with maximum bulk modulus, shear modulus or thermal conductivity. Constituent phases are divided into groups and sensitivity analyses are performed in order to estimate their effects on the variation of the objective function. Changing the elemental properties in the finite element model of the microstructure is performed based on this sensitivity analyses and by imposing volume constraints on the constituent phases. Numerical examples are presented to demonstrate the effectiveness of the algorithm in terms of identification of the phases' boundaries and convergence speed. The proposed approach could potentially be used to design multiphase materials for functional properties other than stiffness and thermal conductivity.