Spatial-varying multi-phase infill design using density-based topology optimization

Porous infill structures have been widely studied and used in additive manufacturing because of their lightweight and excellent mechanical properties. However, without considering graded multi-material infill pattern, existed infill design methods have not yet fully tapped the potential of multiple materials in structural design. In this paper, a systematic multi-phase infill design method is proposed to generate graded multi-material infill structures. The method builds upon a unified multi-material density-based topology optimization framework, in which a modified multi-phase material interpolation formulation is presented to represent the relationship between the stiffness matrix and design variables. To generate spatial-varying and multi-phase structures distributed in the interior of a design domain, the maximum local material volume constraints are imposed on each phase material in the neighborhood of each element in the design domain. A series of relaxations is introduced into the framework to facilitate the implementation of the gradient-based optimization algorithm. The whole design process is performed on a full-size finite element analysis, so it can avoid the separation of scales and naturally guarantee the optimized infills to be smoothly connected. The applicability and effectiveness of the proposed multi-phase infill generation model are then demonstrated by several typical numerical examples with the objective of minimum compliance. •A novel design method for spatially-varying multi-phase infill structures.•The method avoids the length scale separation and sub-structure connectivity issue.•A unified multi-material topology optimization framework is presented.•The approach of imposing local volume constraints on multiphase materials is developed.•The advantages of the obtained graded multi-phase infill structures are demonstrated.