  In this work, a model based on the Physics - Informed Neural Networks (PINNs)
for solving elastic deformation of heterogeneous solids and associated
Uncertainty Quantification (UQ) is presented. For the present study, the PINNs
framework - Modulus developed by Nvidia is utilized, wherein we implement a
module for mechanics of heterogeneous solids. We use PINNs to approximate
momentum balance by assuming isotropic linear elastic constitutive behavior
against a loss function. Along with governing equations, the associated initial
/ boundary conditions also softly participate in the loss function. Solids
where the heterogeneity manifests as voids (low elastic modulus regions) and
fibers (high elastic modulus regions) in a matrix are analyzed, and the results
are validated against solutions obtained from a commercial Finite Element (FE)
analysis package. The present study also reveals that PINNs can capture the
stress jumps precisely at the material interfaces. Additionally, the present
study explores the advantages associated with the surrogate features in PINNs
via the variation in geometry and material properties. The presented UQ studies
suggest that the mean and standard deviation of the PINNs solution are in good
agreement with Monte Carlo FE results. The effective Young's modulus predicted
by PINNs for single representative void and single fiber composites compare
very well against the ones predicted by FE, which establishes the PINNs
formulation as an efficient homogenization tool.
