Single variable-based multi-material structural optimization considering interface behavior

Recently, there is an increasing demand for bonding systems applied to multi-material structures. Among them, adhesives have been widely used to reduce cost and weight instead of traditional mechanical fasteners and welding. However, because the adhesive part can be easily separated under tensile stress, it is necessary to set the proper position of the adhesive in the early design process so that tensile stress does not occur in the adhesive part. This study proposes a method to prevent separation of adhesive bonds between different material phases in topology optimization. The interfacial tension energy density (ITED) is introduced into the objective function to restrict the generation of regions where the material interface with the adhesive is subject to tensile stress. Instead of using multi-design variables based on the number of material phases, the phase section method which uses a single variable is applied for the multi-material topological design. By adding the ITED to the ordinary compliance objective, the proposed method does not require the analysis of the nonlinear material behavior of the bonded areas. Through numerical examples, it is confirmed that the proposed method can offer a simple but effective multi-material design process considering the interfacial behavior.