I am excited to announce our work (with Dr. Oden) on enhancing the accuracy of neural operators using the so-called corrector operator. This work is a culmination of our efforts in using goal-oriented a-posteriori error estimates in Bayesian inference in Jha and Oden (2022), JCP 470, 111575, and recently using a similar idea in Cao et al. (2023), JCP 486, 112104.
Authors - Prashant K. Jha, Timothy Breitzman, and Kaushik Dayal
Journal - Archive for Rational Mechanics and Analysis
Abstract
Journal: International Journal of Fracture
Abstract: A simple nonlocal field theory of peridynamic type is applied to model brittle fracture. The kinetic relation for the crack tip velocity given by Linear Elastic Fracture Mechanics (LEFM) is recovered directly from the nonlocal dynamics, this is seen both theoretically and in simulations. An explicit formula for the change of internal energy inside a neighborhood enclosing the crack tip is found for the nonlocal model and applied to LEFM.
Prashant K. Jha and Robert Lipton
Computer Methods in Applied Mechanics and Engineering, 2019.
https://doi.org/10.1016/j.cma.2019.03.024
Highlights
1. Well-posedness of a general nonlinear state based peridynamic models.
2. A priori numerical convergence rate for finite difference approximations of state based peridynamic models.
3. Numerical verification of convergence rate for samples with growing cracks.
With Robert Lipton. Submitted to Mathematical Models and Methods in Applied Sciences. arXiv link: https://arxiv.org/abs/1710.07661
