A phase field-based systematic multiscale topology optimization method for porous structures design

In this paper, we propose a novel and systematic phase field-based multiscale topology optimization method for porous structures design. The multi-regional microstructural composite and fixed microstructural shapes are adopted to balance the objective and other constraints. The connectivity issue between different microstructures is handled. In the multiscale topology optimization, the macro and micro design variables are updated by the Allen-Cahn type equations which include a reaction-diffusion term, a sensitivity analysis term, a volume constraint term, and a correction term. The correction term is used to keep topologies of macro and micro structures closed to the prescribed structures. We use an efficient merging algorithm to handle the connectivity issue between different microstructures. Based on an interpolation technique of the phase field function and a modified Allen-Cahn equation, this algorithm can smooth the connecting boundaries and satisfy the minimum surface theorem. The final distribution of microstructures keeps the extraordinary physical and mechanical properties for the macrostructure. Some typical cantilever beam, Michell-type structure and Messerschmitt-Bölkow-Blohm beam are performed to verify the effectiveness of our method.