Compliance-based topology optimization of multiple-phase materials related to the scale effect

Abstract

With the rapid advancement of technology, the device's size gradually tends to be miniaturized to the micro or nanoscale. However, the traditional framework based on classical mechanics is no longer sufficient to explain the impact of the scale effects on the mechanical behavior of these miniaturized structures. Furthermore, the increasing demand for multi-phase materials with excellent comprehensive performance also drives the growth of reverse design. Therefore, this study proposes a topological optimization design method for multi-phase materials that considers scale effects. The interpolation model of multi-phase materials utilizes elemental density to establish a mapping relationship with each phase material. The improved couple stress theory incorporates intrinsic characteristic length parameters to account for the scale effect in small-scale structures. Several numerical examples demonstrate that when the macroscopic size of the structure approaches the intrinsic characteristic length parameter, a significant scale effect occurs in the small-scale structure, leading to a redistribution of the topological configuration of the weak-phase material.