Mechanistically informed artificial neural network model for discovering anisotropic path-dependent plasticity of metals

Abstract

The plasticity of metals involves various complicated phenomena that have not been fully discovered or explained by existing theories. The data-driven method provides a new avenue that is different from the traditional methodology and extends the existing understanding of the constitutive behavior of metals. This study proposes an artificial neural network (ANN) model informed by mechanistic features to discover anisotropic path-dependent plasticity. The proposed framework imposed physical and numerical constraints of the constitutive law on a neural network with good interpretability and reliability. The modified return-mapping algorithm was combined with the ANN using an automatic differential technique, where a sub-fully connected neural network was employed to predict the elastoplastic tangent stiffness to ensure the stability of the plastic flow. Moreover, a yield function constructed using a fully connected neural network was adopted for anisotropic and path-dependent yields. The influence of the number of hidden layers and neurons on the final accuracy was also investigated. A metamaterial representative volume element was created to produce sufficient stress–strain response data for the learning purpose of the neural network. After proper training, the proposed method successfully revealed its hidden anisotropic yield and hardening behavior. A comparison with the traditional yield function was also performed using finite element simulations.