# A single Long Short-Term Memory network for enhancing the prediction of path-dependent plasticity with material heterogeneity and anisotropy

arXiv: https://arxiv.org/abs/2204.01466 · HTML: https://mlsanity.com/paper/2204.01466/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 38 references that are in the map.
- First posted on arXiv 29 Mar 2022.

## Builds on (most cited first, 2 of 2)

- [A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materials](https://mlsanity.com/paper/1807.09829/) (2018)
- [MC-LSTM: Mass-Conserving LSTM](https://mlsanity.com/paper/2101.05186/) (2021)

## Built on by (most cited first, 4 of 4)

- [A machine learning-based viscoelastic-viscoplastic model for epoxy nanocomposites with moisture content](https://mlsanity.com/paper/2305.08102/) (2023)
- [Towards scientific machine learning for granular material simulations -- challenges and opportunities](https://mlsanity.com/paper/2504.08766/) (2025)
- [A thermodynamically consistent physics-informed deep learning material model for short fiber/polymer nanocomposites](https://mlsanity.com/paper/2403.18310/) (2024)
- [One-Step Flow Matching for Generative Modeling of Path-Dependent Physical Fields](https://mlsanity.com/paper/2606.22752/) (2026)

## Abstract (arXiv)

This study presents the applicability of conventional deep recurrent neural networks (RNN) to predict path-dependent plasticity associated with material heterogeneity and anisotropy. Although the architecture of RNN possesses inductive biases toward information over time, it is still challenging to learn the path-dependent material behavior as a function of the loading path considering the change from elastic to elastoplastic regimes. Our attempt is to develop a simple machine-learning-based model that can replicate elastoplastic behaviors considering material heterogeneity and anisotropy. The basic Long-Short Term Memory Unit (LSTM) is adopted for the modeling of plasticity in the two-dimensional space by enhancing the inductive bias toward the past information through manipulating input variables. Our results find that a single LSTM based model can capture the J2 plasticity responses under both monotonic and arbitrary loading paths provided the material heterogeneity. The proposed neural network architecture is then used to model elastoplastic responses of a two-dimensional transversely anisotropic material associated with computational homogenization (FE2). It is also found that a single LSTM model can be used to accurately and effectively capture the path-dependent responses of heterogeneous and anisotropic microstructures under arbitrary mechanical loading conditions.