# Hybrid data-driven and physics-informed regularized learning of cyclic plasticity with Neural Networks

arXiv: https://arxiv.org/abs/2403.01776 · HTML: https://mlsanity.com/paper/2403.01776/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 59 references that are in the map.
- First posted on arXiv 4 Mar 2024.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [A new family of Constitutive Artificial Neural Networks towards automated model discovery](https://mlsanity.com/paper/2210.02202/) (2022)
- [Physics informed neural networks for continuum micromechanics](https://mlsanity.com/paper/2110.07374/) (2021)
- [Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology](https://mlsanity.com/paper/2211.08939/) (2022)
- [NN-EUCLID: deep-learning hyperelasticity without stress data](https://mlsanity.com/paper/2205.06664/) (2022)
- [The mixed deep energy method for resolving concentration features in finite strain hyperelasticity](https://mlsanity.com/paper/2104.09623/) (2021)
- [A machine learning based plasticity model using proper orthogonal decomposition](https://mlsanity.com/paper/2001.03438/) (2020)
- [A comparative study on different neural network architectures to model inelasticity](https://mlsanity.com/paper/2303.03402/) (2023)
- [Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics](https://mlsanity.com/paper/2307.02494/) (2023)

## Abstract (arXiv)

An extendable, efficient and explainable Machine Learning approach is proposed to represent cyclic plasticity and replace conventional material models based on the Radial Return Mapping algorithm. High accuracy and stability by means of a limited amount of training data is achieved by implementing physics-informed regularizations and the back stress information. The off-loading of the Neural Network is applied to the maximal extent. The proposed model architecture is simpler and more efficient compared to existing solutions from the literature, while representing a complete three-dimensional material model. The validation of the approach is carried out by means of surrogate data obtained with the Armstrong-Frederick kinematic hardening model. The Mean Squared Error is assumed as the loss function which stipulates several restrictions: deviatoric character of internal variables, compliance with the flow rule, the differentiation of elastic and plastic steps and the associativity of the flow rule. The latter, however, has a minor impact on the accuracy, which implies the generalizability of the model for a broad spectrum of evolution laws for internal variables. Numerical tests simulating several load cases are shown in detail and validated for accuracy and stability.