Micromechanics-Informed Neural Networks for Periodic Homogenization of Thermocondcutive Behavior in Unidirectional Composites with Cylindrically Orthotropic Graphite Fibers

Abstract

A micromechanics-informed neural network framework is developed for homogenization of periodic unidirectional thermoconductive composites with cylindrically orthotropic fibers. The framework hard-imposes the steady-state governing heat conduction equations within the network architecture, enabling accurate capture of singular heat flux fields at the fiber center that are challenging for conventional approaches. In contrast, continuity and periodicity conditions are enforced via boundary collocation points in the loss function. Validation against finite element simulations across a wide range of fiber volume fractions shows that accurate and converged temperature distributions can be achieved after 9000 training epochs using 8-16 harmonic terms. Additional higher-order harmonics are difficult to train reliably and may degrade predictions. While strong agreement is observed in the matrix heat flux distributions, noticeable discrepancies persist in the fiber phase due to varying ability to capture the singular heat flux fields. Furthermore, uniform collocation points converge faster than random points during solution refinement. Finally, transfer learning is employed to accelerate training for new configurations, allowing the network to achieve comparable accuracy after only 2000 training epochs, which is substantially fewer than the 9,000 epochs required when training from scratch.