[HTML][HTML] A review of peridynamic theory and nonlocal operators along with their computer implementations

M Dorduncu, H Ren, X Zhuang, S Silling… - Computers & …, 2024 - Elsevier
This study presents a comprehensive exploration of Peridynamic (PD) theory, with a specific
focus on its theoretical foundations and practical implementations, including various PD …

A physics-informed variational DeepONet for predicting crack path in quasi-brittle materials

S Goswami, M Yin, Y Yu, GE Karniadakis - Computer Methods in Applied …, 2022 - Elsevier
Failure trajectories, probable failure zones, and damage indices are some of the key
quantities of relevance in brittle fracture mechanics. High-fidelity numerical solvers that …

Physics-informed deep neural operator networks

S Goswami, A Bora, Y Yu, GE Karniadakis - Machine learning in modeling …, 2023 - Springer
Standard neural networks can approximate general nonlinear operators, represented either
explicitly by a combination of mathematical operators, eg in an advection–diffusion reaction …

A comprehensive review on the vibration analyses of small-scaled plate-based structures by utilizing the nonclassical continuum elasticity theories

AA Nuhu, B Safaei - Thin-Walled Structures, 2022 - Elsevier
In recent years, mechanical characteristics including vibration, bending, buckling and
postbuckling, stability and instability, etc. of small-scaled structures (such as …

Interfacing finite elements with deep neural operators for fast multiscale modeling of mechanics problems

M Yin, E Zhang, Y Yu, GE Karniadakis - Computer methods in applied …, 2022 - Elsevier
Multiscale modeling is an effective approach for investigating multiphysics systems with
largely disparate size features, where models with different resolutions or heterogeneous …

Learning deep implicit Fourier neural operators (IFNOs) with applications to heterogeneous material modeling

H You, Q Zhang, CJ Ross, CH Lee, Y Yu - Computer Methods in Applied …, 2022 - Elsevier
Constitutive modeling based on continuum mechanics theory has been a classical approach
for modeling the mechanical responses of materials. However, when constitutive laws are …

Peridynamic neural operators: A data-driven nonlocal constitutive model for complex material responses

S Jafarzadeh, S Silling, N Liu, Z Zhang, Y Yu - Computer Methods in …, 2024 - Elsevier
Neural operators, which can act as implicit solution operators of hidden governing
equations, have recently become popular tools for learning the responses of complex real …

A neural network peridynamic method for modeling rubber-like materials

Y Chen, Y Yang, Y Liu - International Journal of Mechanical Sciences, 2024 - Elsevier
Peridynamic (PD) is a powerful tool for simulating the large deformation and failure process
of many types of materials. However, its use in modeling rubber-like materials is limited due …

Prediction of graphene's mechanical and fracture properties via peridynamics

X Liu, P Yu, B Zheng, E Oterkus, X He, C Lu - International Journal of …, 2024 - Elsevier
Although graphene is believed to be the strongest material, many properties of this material
are still worth exploring and discovering, especially the influence of inevitable defects in its …

Machine learning of nonlocal micro-structural defect evolutions in crystalline materials

EAB de Moraes, M D'Elia, M Zayernouri - Computer Methods in Applied …, 2023 - Elsevier
The presence and evolution of defects that appear in the manufacturing process play a vital
role in the failure mechanisms of engineering materials. In particular, the collective behavior …