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

• Published in: Journal of the mechanics and physics of solids 2020-10, Vol.143, p.103972, Article 103972
• Main Authors: Gorji, Maysam B., Mozaffar, Mojtaba, Heidenreich, Julian N., Cao, Jian, Mohr, Dirk
• Format: Article
• Language: English
• Subjects: Axial stress; Bauschinger effect; Complexity; Elastoplasticity; Fully connected neural network; Gated recurrent unit; HAH; Hardening; Machine learning; Model testing; Neural networks; Plane stress; Plasticity; Recurrent neural network; Recurrent neural networks; Strain; Stress-strain relationships; Two dimensional models; Unit cell; Yld2000-2d
• ISSN: 0022-5096; 1873-4782
• DOI: 10.1016/j.jmps.2020.103972

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.