Modified Multi-material Topology Optimization Considering Isotropic and Anisotropic Materials Mixture

This paper describes the element interpolation scheme for multi-material topology optimization (MMTO), which generalizes the existing standard MMTO approach to overcome the inherent limitations of using only isotropic materials with a constant Poisson’s ratio. To address this limitation, the proposed method transforms the MMTO solution in a series of single material topology optimization (SMTO) by stacking multiple elements within the same design cell and assigning each weighted candidate material to an element. Solid Isotropic Material with Penalization (SIMP) equations are defined as weighting factors applied on each candidate material. As a result, anisotropic or isotropic materials with different Poisson’s ratios can be implemented in MMTO, allowing engineers to determine optimized designs that explore the full potential of isotropic and anisotropic materials properties. A thorough discussion of the element interpolation method as well the sensitivity equations are presented in this paper along with two application examples demonstrating its implementation.