Topology optimization with multi-phase length-scale control

Abstract

We present a multi-material density-based topology optimization framework that offers full length-scale control on each of the material phases involved. We represent different material phases by different sets of independent design variables, while avoiding a prohibitive number of constraints, and devise a consistent penalization tailored to multimaterial design. The independent design variables are passed through multi-phase Heaviside projections and the modified material model with penalization to define element densities and material properties. Overfilling is avoided via constraints on element densities which are handled through “sum of powers” aggregation and smoothing to curtail the need for local constraints and the associated computational burden. The proposed framework enables the imposition of individual length scales while avoiding, to a large extent, the issues related to phase mixing at boundaries. It is also amenable to gradient-based optimizers and thus capable of solving large-scale multi-material topology optimization problems. Multiple topology optimization problems, including compliance minimization and design of compliant mechanisms are provided to demonstrate the effectiveness of the proposed framework to cleanly enforce specified length-scales on individual material phases.