A deep-learning based and thermodynamically consistent model for nanoparticle-filled epoxy nanocomposites under ambient conditions

In this work, we propose a physics-informed deep learning (DL)-based constitutive model for investigating epoxy based composites under different ambient conditions. The deep-learning model is trained to enforce thermodynamics principles and ensures a thermodynamic consistent constitutive model. For this, a long short-term memory network is combined with a feed-forward neural network to predict internal variables of the material system, which are needed to characterize the internal dissipation of the material. Another feed-forward neural network is employed to predict the free-energy function, therefore defining the thermodynamic state of the whole system.

The data is directly generated from cyclic loading-unloading experiments conducted on a nanoparticle filled epoxy system. The experiments include diverse ambient conditions e.g. temperature, moisture and nanoparticle volume fraction. Accordingly, the accuracy of the deep-learning model in accurately predicting the material behavior for a material system characterized by a highly nonlinear response with temperature- and moisture dependency is shown. Importantly, the deep-learning model solely utilizes experimental data, demonstrating the capability to capture the complex stress-strain response of the material at hand.

The figure below presents the architecture of our thermodynamic consistent DL model.