On the potential of recurrent neural networks for modeling path dependent plasticity

Maysam B. Gorji, Mojtaba Mozaffar, Julian N. Heidenreich, Jian Cao, Dirk Mohr*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

137 Scopus citations


The mathematical description of elastoplasticity is a highly complex problem due to the possible change from elastic to elasto-plastic behavior (and vice-versa) as a function of the loading path. Advanced physics-based plasticity models usually feature numerous internal variables (often of tensorial nature) along with a set of evolution equations and complementary conditions. In the present work, an attempt is made to come up with a machine-learning based model that can replicate the predictions anisotropic Yld2000-2d model with homogeneous anisotropic hardening (HAH). For this, a series of modeling problems of increasing complexity is formulated and sequentially addressed using neural network models. It is demonstrated that basic fully-connected neural network models can capture the characteristic non-linearities in the uniaxial stress-strain response such as the Bauschinger effect, permanent softening or latent hardening. A neural network with gated recurrent units (GRUs) and fully-connected layer is proposed for the modeling of plane stress plasticity for arbitrary loading paths. After training and testing the model through comparison with the Yld2000-2d/HAH model, the recurrent neural network model is also used to model the multi-axial stress-strain response of a two-dimensional foam. Here, the comparison with the results from unit cell simulations provided another validation of the proposed data-driven modeling approach.

Original languageEnglish (US)
Article number103972
JournalJournal of the Mechanics and Physics of Solids
StatePublished - Oct 2020


  • Fully connected neural network
  • Gated recurrent unit
  • HAH
  • Plasticity
  • Recurrent neural network
  • Yld2000-2d

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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