Calibrating constitutive models with full-field data via physics informed neural networks
This work addresses a long-standing problem in materials science for researchers calibrating models with full-field data, offering a novel method that is incremental but improves efficiency and applicability.
The paper tackles the challenge of calibrating solid constitutive models using full-field experimental data by proposing a physics-informed deep-learning framework that works with the weak form of governing equations. The approach is computationally efficient, handles irregular geometries, and directly ingests displacement data without grid interpolation, demonstrating its potential to shift the paradigm in constitutive model calibration under finite deformations.
The calibration of solid constitutive models with full-field experimental data is a long-standing challenge, especially in materials which undergo large deformation. In this paper, we propose a physics-informed deep-learning framework for the discovery of constitutive model parameterizations given full-field displacement data and global force-displacement data. Contrary to the majority of recent literature in this field, we work with the weak form of the governing equations rather than the strong form to impose physical constraints upon the neural network predictions. The approach presented in this paper is computationally efficient, suitable for irregular geometric domains, and readily ingests displacement data without the need for interpolation onto a computational grid. A selection of canonical hyperelastic materials models suitable for different material classes is considered including the Neo-Hookean, Gent, and Blatz-Ko constitutive models as exemplars for general hyperelastic behavior, polymer behavior with lock-up, and compressible foam behavior respectively. We demonstrate that physics informed machine learning is an enabling technology and may shift the paradigm of how full-field experimental data is utilized to calibrate constitutive models under finite deformations.