Multimaterial stress-constrained topology optimization with multiple distinct yield criteria

Abstract

Composite structures offer unique mechanical and physical properties enabled by material heterogeneity. To harness these properties in stress-constrained topology optimization, the incorporation of multiple materials is necessary. Established studies in the field typically assume the same yield criterion for all the candidate materials while vary their stiffness and strengths. To open up the full design capability for composite structures, we propose a novel yield function interpolation scheme that allows for the simultaneous incorporation of distinct yield criteria and material strengths. Built upon this yield function interpolation scheme, we introduce a stress-constrained topology optimization formulation that handles multiple materials with distinct elastic properties, material strengths, and yield criteria simultaneously. We investigate several two-dimensional and three-dimensional design cases with the objective of minimizing the total volume subjected to stress constraints. The optimized composite designs reveal several fundamental advantages enabled by material heterogeneity, including design space enlargement, stress deconcentration effect, and exploitation of tension–compression strength asymmetry. These advantages lead to composite designs with 10−40% reduced minimized volumes as compared to single-material designs and provide new insights for the discovery of more efficient composite structures.