Modeling finite-strain plasticity using physics-informed neural network and assessment of the network performance

Abstract

Physics-informed neural networks (PINN) can solve partial differential equations (PDEs) by encoding the mathematical information explicitly into the loss functions. In the context of plasticity, discussions of PINN have only focused on small-strain formulations. We present a framework of finite-strain elasto-plasticity for PINN, considering rate-independent isotropic hardening in this work. Details of the model architecture are discussed, including inputs and outputs of the neural network and the construction of the loss function that incorporates equilibrium equations, boundary conditions and constitutive relations. In addition, the overall architecture can learn the constitutive relations from discrete measurements on a stress–strain curve, hence eliminating the need for modeling hardening law in the formulation. We demonstrate the performance of PINN through a numerical example that includes a multi-step loading and unloading history. Moreover, we assess the performance of PINN in terms of its accuracy and robustness under mesh refinement and as a function of the network architecture design. Displacement, Cauchy stress and accumulated plastic strain fields are compared to the finite element results for the same problem for the purposes of this assessment, which is intended to provide insight and guidance for the future designs of PINN for plasticity and related problems in solid mechanics.