A Physics Preserving Neural Network Based Approach for Constitutive Modeling of Isotropic Fibrous Materials

Abstract

We develop a new neural network based material model for discrete fibrous materials that strictly enforces constitutive constraints such as polyconvexity, frame-indifference, and the symmetry of the stress and material stiffness. Additionally, we show that the accuracy of the stress and material stiffness predictions is significantly improved for this neural network by using a Sobolev minimization strategy that includes derivative terms. We obtain a normalized mean square error of 0.15% for the strain energy density, 0.815% averaged across the components of the stress, and 5.4% averaged across the components of the stiffness tensor. This machine-learned constitutive model was deployed in a finite element simulation of a facet capsular ligament. The displacement fields and stress–strain curves were compared to a multiscale simulation that required running on a GPU-based supercomputer. The new approach maintained upward of 85% accuracy in stress up to 70% strain while reducing the computation cost by orders of magnitude.

Nishan Parvez

Affiliated

I work on machine learning, constitutive modeling, and fibrous materials.

Jacob Merson

Assistant Professor of Mechanical Engineering

loves to scale multiphysics simulations onto leadership class supercomputers