Physics-informed neural network frameworks for crack simulation based on minimized peridynamic potential energy

Abstract

Physics-informed neural networks (PINNs), which are promising tools for solving nonlinear equations in the absence of labeled data, have been successfully applied for continuum field approximation in fluid mechanics, solid mechanics, thermodynamics, and other scientific and engineering problems. However, it is equally necessary to solve discontinuous problems such as cracking behaviors in structures and materials, which are challenging to describe using partial differential equations in traditional solid mechanics frameworks. In this work, PINNs are established with the constraint of integral–differential equations in bond-based peridynamic to simulate crack initiation and propagation behaviors in quasi-brittle plates. To solve the cracking behaviors, the initial displacements of the plate are determined by minimizing the total potential energy through the optimization of global network parameters. The subsequent displacements during crack initiation or propagation are characterized by transfer learning to accelerate convergence. The simulated crack paths for four cases with or without precracks are consistent with those obtained in existing studies based on experiments or numerical simulations. Moreover, the effects of network regularization and neuron scales on the nonlinear displacement characterization performance are investigated.