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

TL;DR

This paper demonstrates the use of Physics-Informed Neural Networks (PINNs) to model elastic deformation and uncertainty quantification in heterogeneous materials, showing high accuracy and efficiency compared to traditional finite element methods.

Contribution

The study introduces a PINNs-based framework for mechanics of heterogeneous solids, validating its accuracy and efficiency in capturing stress jumps and predicting effective material properties.

Findings

PINNs accurately capture stress jumps at material interfaces.

The PINNs-based homogenization matches FE results for effective Young's modulus.

UQ results from PINNs align well with Monte Carlo FE simulations.

Abstract

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.