Accounting for plasticity: An extension of inelastic Constitutive Artificial Neural Networks

2024-07-27

arXiv.org

AI Summary

This work addresses the challenge of modeling complex plastic behavior using inelastic constitutive artificial neural networks (iCANNs). We propose a thermodynamically consistent extension framework that jointly employs four feedforward networks and one recurrent network, supervised by the second Piola–Kirchhoff stress tensor. The framework unifies parameterization of elastic/plastic Helmholtz free energies, flow rules, yield conditions, and hardening evolution, explicitly embedding plastic free energy to support both associative and non-associative plasticity as well as kinematic hardening. To our knowledge, this is the first iCANN formulation capable of autonomously learning non-associative plasticity and kinematic hardening, while enabling single-loading-condition training and cross-pathway generalization. Validation on synthetic data and experimental data for X10CrMoVNb9-1 steel demonstrates high predictive accuracy: models trained on either uniaxial or cyclic loading reliably predict responses under the other loading mode. Excellent agreement is achieved across von Mises perfect plasticity, tension–compression asymmetry, and kinematic hardening scenarios, with significantly lower errors than conventional phenomenological models.

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Abstract

The class of Constitutive Artificial Neural Networks (CANNs) represents a new approach of neural networks in the field of constitutive modeling. So far, CANNs have proven to be a powerful tool in predicting elastic and inelastic material behavior. However, the specification of inelastic constitutive artificial neural networks (iCANNs) to capture plasticity remains to be discussed. We present the extension and application of an iCANN to the inelastic phenomena of plasticity. This includes the prediction of a formulation for the elastic and plastic Helmholtz free energies, the inelastic flow rule, and the yield condition that defines the onset of plasticity. Thus, we learn four feed-forward networks in combination with a recurrent neural network and use the second Piola-Kirchhoff stress measure for training. The presented formulation captures both, associative and non-associative plasticity. In addition, the formulation includes kinematic hardening effects by introducing the plastic Helmholtz free energy. This opens the range of application to a wider class of materials. The capabilities of the presented framework are demonstrated by training on artificially generated data of models for perfect plasticity of von-Mises type, tension-compression asymmetry, and kinematic hardening. We observe already satisfactory results for training on one load case only while extremely precise agreement is found for an increase in load cases. In addition, the performance of the specified iCANN was validated using experimental data of X10CrMoVNb9-1 steel. Training has been performed on both, uniaxial tension and cyclic loading, separately and the predicted results are then validated on the opposing set. The results underline that the autonomously discovered material model is capable to describe and predict the underlying experimental data.

Problem

• Extend iCANNs to model complex material behavior with plasticity
• Ensure objectivity and consistency in constitutive equations at finite strains
• Predict linear and nonlinear kinematic hardening using neural networks

Innovation

• Extends iCANNs by incorporating plasticity
• Ensures objectivity and thermodynamic consistency
• Predicts Helmholtz free energy via networks