Learning composite constitutive laws via coupling Abaqus and deep neural network

Abstract

The commercial finite element (FE) code Abaqus is coupled with the deep neural network (DNN) model, namely Abaqus-DNN mechanics system, to learn the constitutive law of the fiber-reinforced composite. The proposed system enables data communication between Abaqus and DNN model, which leverages the versatile FE analysis ability of Abaqus and the powerful machine learning using DNN. Abaqus-DNN enables DNN to learn the constitutive law in a form-free manner. The learned result automatically satisfies the equilibrium and kinematics equations, which avoids inaccuracies associated with the presumed functions in the constitutive laws and guaranteed the learned constitutive law following the laws of physics. The Abaqus-DNN mechanics system was implemented to learn the full set of engineering constants of the constituents of a fiber-reinforced composite. Furthermore, the proposed system was applied to learn the progressive damage constitutive law of a fiber-reinforced composite laminate. The backward propagation equations of the neural network were modified to track the gradient of the loss function from Abaqus to DNN. The results show that Abaqus-DNN can accurately learn constitutive laws based on structural level data. This system provides a generalized approach for learning unknown physics inside a mechanics system by coupling neural network with commercial finite element codes.