A neural network enhanced system for learning nonlinear constitutive law and failure initiation criterion of composites using indirectly measurable data

Abstract A neural network enhanced system containing a subsystem with one or multiple neural networks is proposed. Instead of defining the loss function as the direct output of a neural network model, the proposed method uses the system output, which can be measured from experiments, to define the loss function. The loss function is contributed by the outputs from one or multiple neural network models through a subsystem. As a result, the direct output of the ANN model is not required to be measurable from experiments. A set of new back-propagation equations have been derived for this system. Two examples are given using the proposed system: learning the nonlinear in-plane shear constitutive law and learning the failure initiation criterion of fiber-reinforced composites (FRC). The neural network models in both examples are trained at the lamina level using the measurable experimental responses of laminates. The results obtained from the learned neural network models agree well with the corresponding analytical solutions. The proposed method can be used to train neural network models in a subsystem when only the input and output of the system is measurable.