A thermodynamically consistent physics-informed deep learning material
  model for short fiber/polymer nanocomposites
Betim Bahtiri Behrouz Arash Sven Scheffler Maximilian Jux Raimund Rolfes
This work proposes a physics-informed deep learning (PIDL)-based constitutive
model for investigating the viscoelastic-viscoplastic behavior of short
fiber-reinforced nanoparticle-filled epoxies under various ambient conditions.
The deep-learning model is trained to enforce thermodynamic principles, leading
to a thermodynamically consistent constitutive model. To accomplish this, a
long short-term memory network is combined with a feed-forward neural network
to predict internal variables required for characterizing the internal
dissipation of the nanocomposite materials. In addition, another feed-forward
neural network is used to indicate the free-energy function, which enables
defining the thermodynamic state of the entire system. The PIDL model is
initially developed for the three-dimensional case by generating synthetic data
from a classical constitutive model. The model is then trained by extracting
the data directly from cyclic loading-unloading experimental tests. Numerical
examples show that the PIDL model can accurately predict the mechanical
behavior of epoxy-based nanocomposites for different volume fractions of fibers
and nanoparticles under various hygrothermal conditions.