Machine learning-based constitutive model for metal plasticity

Abstract

This research encompasses two machine learning applications in the domain of metal forming processes. The first study proposes a machine learning-based constitutive model for anisotropic plasticity in sheet metals. A fully connected deep neural network (DNN) is constructed to learn the stress integration procedure under the plane stress condition. The DNN utilizes the labeled training data for feature learning, and the respective dataset is generated numerically based on the Euler-backward method for the whole loading domains. The DNN is trained sufficiently to learn all the incremental loading paths of the input-output stress pair by using advanced anisotropic yield functions. Its performance with anisotropy is evaluated for the predictions of r-values and normalized yield stress ratios along 0-90 degrees to the rolling direction. In addition, the trained DNN is then incorporated in user material subroutine UMAT in ABAQUS/Implicit. Thereafter, the DNN-based anisotropic constitutive model is tested with a cup drawing simulation to evaluate earing profile. The obtained earing profile is compatible with the one from the trained anisotropic yield function. In the second study, the applicability of the DNN-based constitutive model is extended to the non-associated flow rule. This enables the deep neural network (DNN) to predict anisotropic behavior in sheet metals using separate potential and yield functions. Its performance with anisotropy is evaluated for the predictions of r-values along 0-90 degrees to the rolling direction. Also, single-element simulations are conducted by computing tensile and compressive yield stresses. Thereafter, the DNN-based constitutive model is tested with a tube bending simulation to evaluate the mid-cross-sectional geometry of the Magnesium AZ31 tube. The obtained cross-section profile is compatible with that of the theoretical model.