Maximizing the effective Young's modulus of a composite material by exploiting the Poisson effect

Recent studies have shown that the stiffness of composites in one or more directions could increase dramatically when the Poisson's ratios of constituent phases approach the thermodynamic limits. In this paper, we establish a computational framework for the topology design of the microstructure of a composite material whose constituent phases have distinct Poisson's ratios. In this framework, the composite is assumed to be composed of periodic microstructures and the effective mechanical properties are determined through the numerical homogenization method. Topology optimization for maximizing the effective Young's modulus is performed to find the optimal distribution of material phases, subject to constraints on the volume fractions of the constituent phases. Four 3D numerical examples are presented to demonstrate the capability and effectiveness of the proposed approach. Various microstructures of optimized composites have been obtained for different objective functions and for different parameters.