Constitutive model characterization and discovery using physics-informed deep learning

Constitutive models are fundamental blocks of modeling physical processes, where they connect conservation laws with the kinematics of the system. They are often expressed in the form of linear or nonlinear systems of ordinary differential equations (ODEs). Within nonlinear regimes, however, it is often challenging to characterize these constitutive models. For solids and geomaterials, the constitutive relations that relate the macroscopic stress and strain quantities are described using highly nonlinear, constrained ODEs to characterize their mechanical response at different stages of both reversible and irreversible deformation process. A recent trend in constitutive modeling leverages complex neural network architectures to construct model-free material models, however, such complex networks are inefficient and demand significant training data. Therefore, we believe theory-based parametric models of elastoplasticity are still the most efficient and predictive. To alleviate the challenging task of characterization and discovery of such models, here, we present a physics-informed neural network (PINN) formulation for stress-strain constitutive modeling. The main obstacle that we address is to have complex inequality constraints of elastoplasticity theory embedded in the PINN loss functions. These constraints are crucial to find the correct form of the yield surface and plastic flow. We also show that calibration of new datasets can be performed very efficiently and that enhanced performance can be achieved even for the case of discovery. This framework requires a single dataset for characterization. Although we only focus on mechanical constitutive models, similar analogies can be used to characterize constitutive models for any physical process.

Automated summary

Constitutive models are fundamental in modeling physical processes by connecting conservation laws with system kinematics. However, characterizing these models can be challenging, especially in nonlinear regimes. We believe that theory-based parametric elastoplastic models are still the most efficient and predictive.