Compatibility in microstructural topology optimization

Abstract

Microstructural materials with spatially-varying properties, such as trabecular bone tissue, are widely seen in nature. These functionally graded structures possess smoothly changing microscale topologies that enable performance far superior to that of their base material. While the optimization of periodic microstructures has been studied in depth, less attention has been paid to the assembly of optimized microstructures with spatially varying properties. Existing works address this problem by ensuring geometric connectivity between adjacent microstructural unit cells. In this report, we argue that geometric connectivity is insufficient to ensure the continuation of physical properties, and propose the concept of mechanical compatibility. Mechanical compatibility directly examines the effective mechanical properties of the individual cell together with its neighbour. Our approach simultaneously optimizes the mechanical properties of individual microstructures as well as those of neighbouring pairs, so that material connectivity and smoothly varying physical properties are ensured. We demonstrate the application of our method in the design of functionally graded material for implant design, and in the design of both coupled and decoupled multiscale structures.