Length scale control in density-based multi-material topology optimization

In this paper, the length scale control (LSC) methods, including the maximum length scale control (MaxLSC) and the minimum length scale control (MinLSC) for both the solid and void phase, are proposed for density-based multi-material topology optimization. The three-field approach is extended to multi-material topology optimization problems. The local constraints are built by introducing porosity and material rate to achieve MaxLSC for the solid and void phases, respectively. A p-mean function is utilized to aggregate the MaxLSC constraints into a single global one. The MinLSC is proposed based on geometric constraints and the indicator functions with a normalization gradient norm. The optimization formulations and the sensitivity analysis of the related optimization responses are subsequently derived. Four numerical tests demonstrate that the proposed LSC methods are effective to control the feature length scales and contribute to improving the manufacturability of the optimized structures. The length scales of the joints between different materials can be effectively controlled by the proposed LSC constraints for the entire solid phases. Besides, the LSC constraints are found to achieve diverse topology designs and achieving structural redundancy.