Physics-Informed Machine Learning and Uncertainty Quantification for Mechanics of Heterogeneous Materials

A model based on the Physics-Informed Neural Networks (PINN) for solving elastic deformation of heterogeneous solids and associated Uncertainty Quantification (UQ) is presented. For the present study, the PINN Modulus framework developed by Nvidia is utilized, wherein we implement a module for mechanics of heterogeneous solids. We use PINN 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 and fibers 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 PINN can capture the stress jumps precisely at the material interfaces. Additionally, the present study explores the advantages associated with the surrogate features in PINN via the variation in geometry and material properties. The presented UQ studies suggest that the mean and standard deviation of the PINN solution are in good agreement with Monte Carlo FE results. The effective Young’s modulus predicted by PINN for single representative void and single fiber composites compare very well against the ones predicted by FE.