Material interface control in multi-material topology optimization using pseudo-cost domain method

The recent drive for producing lightweight and high performance designs on reduced timelines has promoted the need for computational design generation tools such as Multi-Material Topology Optimization (MMTO). However, MMTO has drawn some industry skepticism as it assumes different material elements to be perfectly fused together. To address this concern, in this article, a novel pseudo-cost domain (PCD) method is proposed which mathematically determines individual material interfaces in MMTO solutions. The proposed methodology employs a user defined joint cost model to weigh the distinct material interfaces relative to each other. An innovative approach to tailor the MMTO design considering the relative cost of each material interface is presented. The proposed methodology can consider any number of materials and their respective interfaces, and it is defined in such a way that increasing the number of materials has minimal effect on computational time. The methodology is formulated in a smooth and differentiable manner and the sensitivity expressions required by gradient-based optimization solvers are presented. A series of example problems are provided to demonstrate the efficacy of the proposed methodology.