Multi-material and strength-oriented microstructural topology optimization applied to discrete phase and functionally graded materials

Structural optimization plays an important role in lightweight construction, and stresses need to be controlled to avoid material failure. The multi-material design setting offers additional design freedom which can lead to structures with improved strength and stiffness properties compared to the single-material case. The present work addresses topology optimization of a periodic composite material unit cell, with properties predicted by homogenization, using strength and stiffness design criteria, under bulk and mixed loading cases. Plane stress and linear behavior are assumed. The compliance minimization with mass constraint problem is revisited here, but the paper focus is on multi-material stress-based topology optimization. Specifically, the maximal von Mises stress is minimized in the unit-cell where two solids are mixed amidst void. Depending on the material interpolation law settings, two design solutions are investigated. On one hand, the two solids coexist being bonded together across sharp interfaces. On the other hand, a functionally graded material is obtained as an extensive smooth variation of material properties on account of varying composition's volume fractions of both solids throughout the design domain. A parallel MMA version is proposed to efficiently deal with several design constraints. The compliance-based optimization results show that multi-material microstructures can be stiffer compared to single-material ones for the same mass requirement. Regarding the stress-based problem, lower stress peaks are obtained in bi-material design solutions and, specially, in the case of graded material solutions. The latter approximates a fully stressed design which excels in stress mitigation. Therefore, the multi-material setting impacts favorably on structural performance, in both stiffness and strength-oriented designs.