Accounting for plasticity: An extension of inelastic constitutive artificial neural networks

In this work, we extend the framework of inelastic constitutive artificial neural networks (iCANNs) by incorporating plasticity. Thereby, we increase their applicability to capture more complex material behavior by solving the underlying inequality constraints associated with plasticity, aiming to automatically discover the formulation that matches the experimental data most accurately. Learning on stress–strain data, our approach enables the automatic discovery of the constitutive equations for elasto-plastic materials – including the identification of the material parameters and the underlying functional forms of the Helmholtz free energy, yield function and evolution equations for the inelastic deformations including linear and nonlinear kinematic hardening. These are captured using feed-forward neural networks. The proposed methodology ensures objectivity, material symmetry, and thermodynamic consistency, providing a robust and interpretable basis for automatic model discovery at finite strains. Investigation of our model’s prediction showed that the extended iCANNs successfully predict both linear and nonlinear kinematic hardening behavior based on experimental and artificially generated datasets, showcasing promising capabilities of this framework. Nonetheless, challenges remain in fully capturing complex yield criteria – such as those exhibiting tension–compression asymmetry – and predicting complex nonlinear hardening.