Interface-aware topology optimization for multi-material structures via density penalization

With advances in topology optimization and additive manufacturing, complex multi-material structures with monolithic integration have become feasible. However, interfaces between heterogeneous materials are critical performance-sensitive regions, making it essential to incorporate interfacial effects at the structural design stage. Conventional multi-material topology optimization often overlooks the prescribed interfacial effective properties, thus this paper presents a topology optimization framework that jointly accounts for multi-materials and the effective material properties of transition interfaces between the prescribed material pairs. During the optimization process, a density-penalization scheme implicitly identifies interfacial transition regions. Building on this, a generalized multi-material interpolation model that incorporates interfacial properties enables controllable assignment of both base-material and interfacial material properties. In addition, an analytical relation between the identified interface thickness and the control parameters is established, allowing flexible control of the interface thickness. Across a suite of 2D and 3D cases with diverse boundary conditions and objectives, the proposed method produces crisp interfaces with stable convergence and yields clear topology layouts.