Learning viscoplastic constitutive behavior via physics-informed recurrent neural network

A novel physics-informed recurrent neural network (PIRNN) model has been developed for data-driven constitutive modeling of metallic materials under high-strain-rate loading. The proposed PIRNN framework integrates a gated recurrent unit (GRU) network and a fully connected neural network to capture the rate-dependent stress-strain behavior directly from synthetic stress and strain sequences generated from the Johnson-Cook constitutive model. Notably, the inherent memory capability of the GRU model enables implicit representation of arbitrary loading history, without the need for explicitly accounting for internal state variables or prescribed constitutive relations, while the fully connected neural network is utilized to estimate Helmholtz free energy under general loading conditions. Thermodynamic admissibility is ensured by enforcing Helmholtz free energy positivity and the dissipation inequality within the loss function. Validation at the material point level against direct numerical solutions and experimental data demonstrates the accurate predictive capability of the PIRNN under both multiaxial and uniaxial loading conditions. The PIRNN is further implemented in ABAQUS for structural simulations to demonstrate its applicability in structural analyses.