Data-driven nonparametric identification of material behavior based on physics-informed neural network with full-field data

Abstract

A Physics-Informed Neural Network (PINN) model is developed to extract material behavior from full-field displacement data. The PINN model consists of independent networks describing mechanical fields such as displacement, deformation gradient, stress, and strain energy density function. The displacement and deformation gradient networks learn from the deformation data of a specimen, while the stress and material networks predict the stress distribution within the specimen and learn the behavior of the target material, respectively. Each mechanical field should satisfy the physics laws of momentum balance, compatibility, constitutive relations, and boundary conditions. The constraints are wrapped up in the loss function, and the weights and biases of each hidden layer are determined by minimizing the loss function. This study introduces a two-stage learning strategy to deal with the minimization process, which is a multi-objective optimization problem. The accuracy of the proposed method is verified for linear elastic, power-law, and incompressible hyperelastic materials. The data-driven identification method successfully identifies the response of target materials in uniaxial tension, simple shear, and tension-shear-coupled loading cases. The robustness of the proposed method is verified on full-field data with noise and missing points. Data-driven identification can handle full-field data with missing points and maintain a reasonable accuracy level as the noise amplitude increases. Furthermore, data-driven identification results of an incompressible hyperelastic material are compared with conventional parametric identification results. The proposed method has advantages over the conventional method as it requires no predefined model. The results indicate that the data-driven identification method can be applied to new materials without a developed constitutive model or materials with manufacturing uncertainty.