The study and application of Topology Optimization (TO) has experienced great maturity in recent years, presenting itself as a highly influential and sought-after design tool in both the automotive and aerospace industries. TO has experienced development from single material topology optimization (SMTO) to multi-material topology optimization (MMTO), where material selection is simultaneously optimized with material existence. Today, MMTO for standard structural optimization responses are well supported. An additional and vital response in the design of structures is that of stress. Stress-driven or stress-controlled optimization techniques for SMTO are well understood and have been well-documented, evidenced by both published works and its availability in multiple commercial solvers. However, its integration into MMTO frameworks has not yet achieved reliable levels of accuracy and flexibility. The principal limitation of existing stress-constrained MMTO methodologies is the inability to consider candidate material-specific stress limits. Another limitation is that candidate materials cannot have different Poisson’s ratios. Herein, the study of stress-constrained MMTO is extended to consider material-specific yield stresses by introducing a novel stress limit interpolation scheme on P-norm aggregation scheme. Moreover, a stress correction method is extended from SMTO to MMTO, to avoid the stress overestimation issue. In support of the discussion on the constraint and its characteristics, its sensitivities are derived. The proposed method is examined on both 2D and 3D models, including the comparison to the results obtained by the existing commercial solver and on models with more than one million elements or multiple load cases to present the effectiveness of the proposed method.
