Improving the joint quality in density-based multi-material topology optimization with minimum length scale control

In this paper, we delve into the appearance of sharp ‘V’ features at joint areas in multi-material topology optimization, originating from independent minimum length scale control. To mitigate these undesirable features, three approaches have been studied: a hybrid strategy combining independent control with entire void control for parallel distributions, a fusion of independent control and entire solid control for parallel and wrapped distributions, and a local relaxation method employing a two-step filtering scheme. The modified minimum length scale controls for multi-material problems are proposed based on geometric constraints and the indicator functions with a normalization gradient norm. To validate the effectiveness of these methods, four numerical tests have been conducted. The results indicate that the combinations of two minimum length scale controls cannot achieve the parallel distribution and wrapped distribution due to the limited ability to modify the material layout. While local relaxation is feasible, which results in a significant reduction in stress concentration at joint areas.