Topology optimization of multi-material structures considering a piecewise interface stress constraint

Abstract

Topology optimization for multi-material structures has become an important and hot research topic due to their great application potential in modern industries. Unfortunately, most existing multi-material topology optimization methods assume that the interface is perfectly bonded, and those that do not, ignore the strength difference between different interfaces, limiting their application in the design of multi-material structures with more than two solid phases. In this study, a multi-material topology optimization method considering a tension/compression-asymmetric piecewise interface stress constraint is proposed to improve the overall interface strengths of the multi-material structure under the SIMP method framework. Firstly, a new interpolation scheme is developed to identify interfaces between two arbitrary materials and classify the interfaces into different pieces based on the two neighbor materials. Then, a novel piecewise interface stress constraint is developed to describe different targeted strengths at multiple material interfaces. In this constraint, the equivalent interfacial stress considering the tension/compression-asymmetric characteristics is defined by tensile stresses and shear stresses at material interfaces. The maximum stresses at material interfaces are measured by the global p-norm aggregation function which makes imposing the constraint easy. After that, the proposed piecewise tension/compression-asymmetric interface stress constraint is introduced into multi-material topology optimization for compliance minimization. The sensitivity analyses are derived by the adjoint method. Several benchmark 2D examples are provided to discuss the influence of some parameters on optimization problems, such as the interface width, strength scaling factor and the filter radii. Other numerical examples include complex 3D problems and problems involving more than three materials. In all examples, the results show that the proposed algorithm with the tension/compression-asymmetric piecewise interface stress constraint can effectively control interface stress levels and improve structural safety.