Mixed form based physics-informed neural networks for performance evaluation of two-phase random materials

Evaluation of material performance is crucial in establishing processing-structure-property (PSP) relationships in material design. Finite element method (FEM) is commonly used to solve the mechanical properties of materials, but its application for two-phase random materials (TRMs) is limited due to the inherent randomness and complexity of their microstructures which pose significant challenges to mesh generation and computational costs. To this end, this work proposes a comprehensive computational framework for assessing the mechanical properties of TRMs. The random field level cutting method is utilized to reconstruct the equivalent statistical microstructure of the corresponding material. Then, the mixed form based physics-informed neural network (MPINN) is employed to solve the strongly nonlinear field variables of TRMs with linear elastic and elastic-plastic constitutive laws. This approach accurately captures the sharp field variable gradient and plastic strain without requiring high-order derivatives. Furthermore, a phase boundary refinement sampling method is proposed, which halves the computational cost markedly. Finally, transfer learning and surrogate model are introduced to extend the PINN computing framework enabling efficient evaluation of mechanical properties for various microstructures and boundary conditions. In comparison with FEM, results demonstrate the accuracy and high generalization ability of the proposed PINN framework. This framework has broad application prospects in material design, greatly facilitating the performance evaluation of TRMs with complex microstructures.