A novel neural-network non-ordinary state-based peridynamic method for large deformation and fracture analysis of hyperelastic membrane

This paper presents a novel neural network non-ordinary state-based peridynamic (NOSB PD) algorithm for large deformation and fracture analysis of hyperelastic membranes. A non-local membrane theory has been developed by approximating the curved horizon of the membrane as a flat surface and applying the plane stress assumption locally. This allows the simulation of the membrane structure using a single layer of material points, simplifying implementation, improving efficiency, and avoiding volume locking. In the framework of NOSB PD, the deformation gradients are represented by their corresponding bond vectors based on the non-local geometry relationship. Then, the nonlinear bijection between bond vectors and force density is obtained using a developed neural network model. This approach successfully overcomes the zero-energy problem and significantly improves the efficiency. Three representative numerical examples: out of plane deformation, out of plane loading crack propagation and penetrating of a ball are simulated to validate the developed algorithm. The results demonstrate that the developed method can accurately and efficiently achieve the large deformation, out of plane tearing, wrinkle as well as fracture of hyperelastic membranes.