A stepwise physics‐informed neural network for solving large deformation problems of hypoelastic materials

Abstract

Physics‐informed neural network (PINN) has been widely concerned for its higher computational accuracy compared with conventional neural network. The merit of PINN mainly comes from its ability to embed known physical laws or equations into data‐based neural networks. However, when dealing with the rate‐dependent nonlinear problems, such as elasto‐plasticity with loading and unloading and hypoelastic large deformation, the conventional PINN cannot obtain satisfactory results. In this article, a stepwise physics‐informed neural network (sPINN) is proposed to solve large deformation problems of hypoelastic materials. The whole process of sPINN can be divided into a series of time steps. In each time step, the rate constitutive equation expressed by Hughes‐Winget algorithm and momentum governing equation are incorporated into the loss function as physical constraints. The displacement and stress fields can be resolved by completing the training process of each time step. Three numerical examples are designed to validate the proposed method by comparing with the solutions of FEM. The results show that sPINN can accurately resolve the displacement and stress fields in path‐dependent large deformation problems. Furthermore, the performance of the sPINN on small data sets are also discussed, which illustrates that sPINN is more capable of predicting the global solution on small data sets as compared with conventional artificial neural network.

An implicit Updated Lagrangian Fragile Points Method with a support domain refinement scheme for solving large deformation problems

“…Substituting the definition d𝚪 = ndΓ, t = 𝛔n and Equations ( 23) and (24) into Equation ( 22), one obtains, .…”