Multiphase topology optimization for the design of porous metamaterials with local volume constraint

This paper presents a novel multiphase approach for topological design of porous metamaterials. Firstly, a new interpolation scheme based on partition-of-unity mapping is proposed. The scheme is employed into the design of periodic metamaterials with specified expectation on effective properties. Due to the periodicity, the design domain is defined in a Representative Unit Cell (RUC) - which represents the repeated pattern - such that the effective (or homogenized) elastic tensor is evaluated by the Strain Energy Method (SEM). In order to reduce the computational effort, the pattern is assumed to be symmetric, which is equivalent to finding metamaterials with orthotropic behavior. The allowed amount of each material is given via upper bound constraints on global volume fraction. The pore size is further controlled by requiring local volume constraint on each material phase. Via several numerical examples, which differ from each other in terms of objective function and the amount of each material phase, the feasibility of the proposed approach is demonstrated.