Session: 12-05-02: Data-Enabled Predictive Modeling, Scientific Machine Learning, and Uncertainty Quantification in Computational Mechanics

Paper Number: 99105

99105 - Calibrating Constitutive Models With Full-Field Data via Physics Informed Neural Networks 

The Virtual Fields Method (VFM) and Finite Element Model Updating (FEMU), among other inverse problem methodologies, have shown success in calibrating constitutive model parameterizations for various nonlinear material models. However, VFM faces difficulties when only ingesting full-field surface data for specimens where plane-stress assumptions break down, and FEMU remains challenging when calibrating complex models where computational inefficiencies of the inverse problem are intractable. In this work, we use emerging physics-informed machine learning techniques rather than the aforementioned traditional approaches to calibrate constitutive models in large deformation scenarios using full-field experimental data. Physics-informed neural networks (PINNs) can utilize measured data for model calibration while approximately maintaining the known physical laws of the system. PINNs as a computational tool are meshless, with collocation points that are unconnected, meaning there is no need for interpolation strategies between the full-field measurement grid and the computational grid. In a PINN inverse problem, the unknown material parameters are added to the solution basis like VFM. Rather than shape functions, the solution basis in the case of PINNs are the weights and biases of the neural network. Classical PINNs typically work in terms of the strong form of the governing equations and penalize boundary conditions (BCs) in a weak sense. This approach can make imposing the numerous traction-free boundary conditions in a solid mechanics boundary value problem (BVP) difficult and furthermore it can have large effects on the solution displacement field by having errors in the displacement BC. Also working in the strong form requires enough smoothness in the activation functions and a fine enough sampling of collocation points to accurately resolve the second derivatives appearing in the governing equations of motion. Our method utilizes a combination of an energy formulation and the principle of virtual work with displacement BCs enforced exactly.  In this way we have reduced the smoothness requirements and removed several of the objectives from the loss function involving BCs. Traction free BCs are also satisfied by construction. We formulate a loss function with standard error metrics along with a physics-informed term to minimize the error between observed and predicted data while persevering the balance of momentum approximately. This approach is demonstrated using synthetic data, generated from FEM simulations, representative of full-field experimental data for exemplar problems of materials undergoing large heterogenous deformation to calibrate several hyperelastic constitutive models. We will also present preliminary results utilizing digital image correlation experimental data on simple experimental specimen geometries.

Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525 SAND2022-8416 A

 

Presenting Author: Craig Hamel Sandia National Laboratories

Presenting Author Biography: Dr. Craig Hamel received his Ph.D. in mechanical engineering in 2020 from the Georgia institute of technology. He has since since been working at Sandia National Laboratories in a number of research areas revolving around the modeling of the solid mechanics behavior of materials and the numerical implementation of those models. He has recently begun working in the vein of scientific machine learning with an emphasis on applications in solid mechanics.

Authors:

Craig Hamel Sandia National Laboratories
Sharlotte Kramer Sandia National Laboratories
Kevin Long Sandia National Laboratories