Stress Representations for Tensor Basis Neural Networks: Alternative Formulations to Finger–Rivlin–Ericksen

Author:

Fuhg Jan N.11,Bouklas Nikolaos1,Jones Reese E.2

Affiliation:

1. Cornell University Department of Mechanical Engineering, , Ithaca, NY 14853

2. Sandia National Laboratories Mechanics of Materials Department, , 7011 East Avenue, Livermore, CA 94550

Abstract

Abstract Data-driven constitutive modeling frameworks based on neural networks and classical representation theorems have recently gained considerable attention due to their ability to easily incorporate constitutive constraints and their excellent generalization performance. In these models, the stress prediction follows from a linear combination of invariant-dependent coefficient functions and known tensor basis generators. However, thus far the formulations have been limited to stress representations based on the classical Finger–Rivlin–Ericksen form, while the performance of alternative representations has yet to be investigated. In this work, we survey a variety of tensor basis neural network models for modeling hyperelastic materials in a finite deformation context, including a number of so far unexplored formulations which use theoretically equivalent invariants and generators to Finger–Rivlin–Ericksen. Furthermore, we compare potential-based and coefficient-based approaches, as well as different calibration techniques. Nine variants are tested against both noisy and noiseless datasets for three different materials. Theoretical and practical insights into the performance of each formulation are given.

Funder

Air Force Office of Scientific Research

National Nuclear Security Administration

Publisher

ASME International

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