A new multi-material level set topology optimization method with the length scale control capability

Multi-material level set topology optimization methods conventionally rely on the overlap of multiple level set functions to realize the multi-material structural representation. However, this representation may produce redundant material phases and the signed distance information is no longer available within the individual material regions. To fix these issues, a new multi-material level set topology optimization method is proposed in this paper, where m level set functions represent m material phases plus the void, and the signed distance information is straightforwardly available in each material phase. To be specific, each level set function corresponds to a material phase and the overlapping areas are filled with an artificial material type, the property of which is weaker than any of the involved material types. This artificial material plays the role of penalizing the overlap areas to vanish, which is different from the close-to-zero property material type for the void. Hence, the optimization process starts with any multi-level set interpolated input and the overlapping areas will gradually vanish. Based on this new method, we have successfully realized the component length scale control on multi-material structures and innovatively, an approach has been proposed to realize the uniform component thickness control without need of pre-specifying the thickness target.