Material model calibration for elastoplasticity with physics-informed recurrent neural networks

Abstract

Material model calibration often requires inverse analysis through optimization, which poses difficulties even for the simplest material models. To compound the difficulty, the constitutive models for materials exhibiting elastoplastic characteristics are described with highly nonlinear equations and inequalities, creating significant challenges in identifying material parameters. Physics-informed neural networks (PINNs) have recently emerged as a promising method for addressing forward and inverse problems. The method directly integrates physical laws into the loss function of neural networks, making the network inherently physics-aware. In the context of material model calibration, material parameters are treated as trainable parameters within the network. During the training process, PINNs optimize trainable material parameters to fit the observed data, while satisfying the governing physical laws. In this work, we leverage recurrent neural networks to account for the history-dependent behaviors of plasticity, generating the sequence of solutions at measured time points. Elastoplastic constitutive models, along with conservation laws and boundary conditions, are embedded into the loss function to ensure the generated solutions are physically consistent. The method's effectiveness is validated for two classical plasticity models: the von Mises model with hardening and the pressure-dependent Drucker-Prager model. The plastic parameters are identified based on global force-displacement curves and limited local displacement measurements. To enhance practicality, we employ transfer learning to accelerate the convergence of training. Specifically, offline pre-trained models are fine-tuned during the online training stage to adapt to materials with new parameters.