A data-driven physics-constrained deep learning computational framework for solving von Mises plasticity

Abstract

Current work presents an efficient data-driven Physics Informed Neural Networks (PINNs) computational framework for the solution of elastoplastic solid mechanics. To incorporate physical information for the elastoplastic problem, a multi-objective loss function has been carefully designed consisting of the residual of governing partial differential equation (PDE), constitutive relations, flow rules, consistency conditions, and various boundary conditions. In addition, data-driven physical knowledge fitting terms from the high-fidelity Finite Element Method (FEM) solutions for various elastoplastic field variables have been included for the construction of the total loss function. Utilizing multiple densely connected independent ANNs, the model obtains the elastoplastic solution by minimizing the proposed loss function. To demonstrate the strength of the proposed model, two test cases including von Mises perfectly plastic and isotropic linear hardening models are solved under plane-strain condition. Performance in terms of accuracy and robustness illustrates the superiority of the current framework showing excellent agreement with numerical solutions. Furthermore, for better accuracy of field variables with a lesser degree of data-driven estimate and accelerated training, the applicability of transfer learning (TL)-based approach has been illustrated to extend the solution for different sets of boundary conditions and material parameters. The present work highlights an efficient application of the custom-design PINNs model that leverage features from the data-driven solutions to guide the construction of an accurate and robust neural network for the solution of elastoplastic problems.