A fully physics-informed and microstructurally interconnected multi-scale topology optimization method within the phase-field framework

In this paper, we propose a fully physics-informed and microstructurally interconnected multi-scale topology optimization method within the phase-field framework. The proposed approach establishes a bi-scale coupled alternating optimization architecture to achieve a fully physics-driven multi-scale design through the co-evolution of macro-micro coupled displacement neural networks and macro-micro coupled phase-field neural networks. By integrating microstructural effects into the macro-scale response via homogenization theory, a multi-scale coupled energy functional is constructed. Specifically, the physical loss of the coupled macro-micro displacement neural networks is formulated according to the principle of minimum potential energy and homogenization theory. Simultaneously, a multi-scale phase-field energy functional is introduced within the phase-field framework, where a connectivity-index penalty term is incorporated into the loss function of the coupled macro-micro phase-field neural networks. This formulation incorporates the coupled multi-scale physical relations into the network training process. Furthermore, macroscopic single-scale pre-optimization is performed to initialize the subsequent multi-scale optimization. Automatic differentiation is employed to circumvent the complex sensitivity analysis process. Various numerical experiments demonstrate the validity and effectiveness of the proposed method.