A level-set based multi-material topology optimization method using a reaction diffusion equation

•A multi-material topology optimization method using a reaction diffusion equation.•Modified Multi-material Level Set (MM-LS) topology description model.•Controllable geometrical complexity of optimal solutions.

A level-set based multi-material topology optimization method using a reaction diffusion equation is proposed in this paper. Each phase is represented by a combined formulation of different level set functions. This description model is modified from Multi-Material Level Set (MM-LS) topology description model. With a total number of MM level set functions, this approach provides a representation of MM materials and one void phase (totally M+1M+1 phases). By this approach, the mathematic model of the multi-material topology optimization problem using a reaction diffusion equation is established. With this model, the geometrical complexity of optimal solutions can be easily controlled by appropriately setting a regularization parameter. Some implementation details for solving this model are also presented in this paper. Finally, several typical numerical examples are shown to confirm the effectiveness of the proposed method.