A thermodynamics-regularized recurrent neural network framework for coupled elastoplastic damage: Invariant-based formulation and finite element implementation

Neural constitutive models offer a flexible route for path-dependent materials but remain challenged by thermodynamic violations, limited extrapolative robustness, and implicit finite element deployment. This study develops a thermodynamics-regularized recurrent neural network (TRNN) for coupled elastoplastic-damage behavior of quasi-brittle geomaterials. The model operates in stress–strain invariant space, using a gated recurrent unit to encode loading history and two neural networks to represent Helmholtz free energy and mechanical dissipation. Stress is recovered from the learned free energy, while the energy-dissipation relation and non-negative dissipation condition are imposed as soft regularizers. The trained TRNN is reconstructed in Fortran and implemented in Abaqus/Standard through a UMAT, with a perturbation-based numerical Jacobian approximation approximating the material Jacobian. Validation using two synthetic elastoplastic-damage datasets and laboratory triaxial compression data shows accurate stress prediction, improved extrapolative robustness, and favorable dissipation behavior relative to a purely data-driven RNN. Single-element and tunnel-excavation analyses further demonstrate stable finite element deployment; on the finest mesh, relative errors in Mises stress, vertical displacement, and microscopic damage are all below 0.1%. The framework provides a practical route from thermodynamics-regularized constitutive learning to implicit finite element analysis.