Concurrent multi-phase and multiscale topology optimization of fiber-reinforced composites

Fiber-reinforced composites (FRCs) are not only used in aerospace, automobile, and civil engineering, but also widely exist in the biological tissues of animals and plants. Due to their heterogeneity, anisotropy, and structural hierarchy, design optimization of structures made of FRCs remains a challenge. In this paper, we propose a concurrent multi-phase topology form-finding approach for FRCs based on an extended multiscale finite element method. The macroscopic structural topology, the microscopic distributions of multi-phase materials, and the fiber orientations are considered as independent design variables, which are concurrently optimized through a gradient-based algorithm. A mathematical interpolation model is used to describe the constitutive relations of materials at different structural levels. The compliance minimization problems are considered as an example. Sensitivity analyses of both macroscopic and microscopic design variables are performed. This approach can guarantee the connectivity between neighboring substructures, which is of significance in, e.g., additive manufacturing and biomechanical morphogenesis. Several numerical examples are provided to examine the effectiveness of the proposed approach. The results show that this approach is capable of generating high-performance multi-material, multiscale topological designs of FRCs, which have clear boundaries at different structural levels. This work holds potential applications in the optimization of heterogenic and hierarchical structures.