Multi-material topology optimization considering arbitrary strength and yield criteria constraints with single-variable interpolation

Material heterogeneity gives composite constructions unique mechanical and physical qualities. Combining multiple materials takes full use of these features in stress-constrained topology optimization. Traditional research in this field often assumes a consistent yield criterion for all possible materials but adapts their stiffness and strengths accordingly. To cope with this challenge, an innovative single-variable interpolation approach is proposed to enable the simultaneous inclusion of distinct yield criteria and material strengths. A stress-constrained topology optimization formulation is presented based on this yield function interpolation method, which can independently support various materials with different elastic characteristics, material strengths, and yield criteria. Then, the large-scale problem of local stress constraints can be effectively solved by the Augmented Lagrangian (AL) method. Several two-dimensional (2D) and three-dimensional (3D) design scenarios are investigated to reduce the overall mass of the structure while considering stress constraints. The optimal composite designs exhibit several crucial benefits resulting from material heterogeneity, including the enlargement of the design possibilities, the dispersion of stress, and the utilization of asymmetry in tension-compression strength.