Topology optimization of multi-material structures with explicitly graded interfaces

The rapid development of additive manufacturing (AM) offers new opportunities to fabricate multi-material structures, whose performance can be optimized by the integrated design of multiple materials distribution and their interface behaviors. However, the graded-interface assumption between different materials often caused some numerical difficulties during topology optimization, e.g., poor applicability in weak interface and difficulty in accurately controlling interface width. This work develops a new element-based topology optimization algorithm by explicitly considering strong, weak or intermediate interfaces, and the interfacial width can also be controlled precisely. Under the explicit expression of a graded interface, a linear multi-material interpolation scheme is proposed to gradually achieve realistic graded physical field within the interfacial zone, where the interdiffusion or reaction inevitably happens and leads to the gradual transition of the interface property. The compliance minimization of multi-material structures with different types of graded interfaces is formulated under multiple volume fraction constraints. The sensitivity of the objective function and constraints with respect to design variables are derived. Numerical examples demonstrate that the optimized designs resulting from the proposed method always achieve a lower compliance, compared with those of the traditional multi-material designs. A phase diagram is presented to describe the sensitivity of the topological design on the interface behavior.