Multi-material topology optimization considering interface behavior via XFEM and level set method

In most of the existing topology optimization studies of multi-material structures, the interface of different materials was assumed to be perfectly bonded. Optimal design based on the perfect-interface assumption may introduce the risk of failure caused by interface debonding. This paper presents an efficient multi-material topology optimization strategy for seeking the optimal layout of structures considering the cohesive constitutive relationship of the interface. Based on the color level set method to describe the topology and the interface, the interface behavior is simulated by combining the extended finite element method (XFEM) and the cohesive model on fixed mesh. This enables modeling of possible separation of material interfaces, and thus provides a more realistic model of multi-material structures. Furthermore, this interface modeling technique avoids the difficulty of re-meshing when tracking the moving cohesive interface positions during the optimization process. In the topology optimization model, the normal velocities defined on the level set points are considered as design variables. In conjunction with the adjoint-variable sensitivity analysis, these design variables are updated by using the mathematical programming approach and then used to interpolate the boundary velocities. These boundary velocities are extrapolated to the whole domain with the fast marching method and used to advance the structural boundary through the Hamilton-Jacobi equation. This topology optimization technique can handle multiple constraints easily in the framework of level set method and at the same time preserve the signed distance property of the level set functions. Two numerical examples are given to demonstrate the effectiveness of the present method. It is also revealed that the optimal design considering interface behavior may exhibit tension/compression non-symmetric topology, in which material interfaces mainly undergo compression.