TY  - JOUR
A1  - Rabczuk, Timon
A1  - Zhuang, Xiaoying
A1  - Oterkus, Erkan
T1  - Editorial: Computational modeling based on nonlocal theory
JF  - Engineering with Computers
N2  - Nonlocal theories concern the interaction of objects, which are separated in space. Classical examples are Coulomb’s law or Newton’s law of universal gravitation. They had signficiant impact in physics and engineering. One classical application in mechanics is the failure of quasi-brittle materials. While local models lead to an ill-posed boundary value problem and associated mesh dependent results, nonlocal models guarantee the well-posedness and are furthermore relatively easy to implement into commercial computational software.
KW  - Computersimulation
KW  - Mathematische Modellierung
KW  - computational modeling
KW  - nonlocal theory
Y1  - 2023
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20230517-63658
UR  - https://link.springer.com/article/10.1007/s00366-022-01775-7
VL  - 2023
IS  - Volume 39, issue 3
PB  - Springer
CY  - London
ER  - 
TY  - JOUR
A1  - Ren, Huilong
A1  - Zhuang, Xiaoying
A1  - Oterkus, Erkan
A1  - Zhu, Hehua
A1  - Rabczuk, Timon
T1  - Nonlocal strong forms of thin plate, gradient elasticity, magneto-electro-elasticity and phase-field fracture by nonlocal operator method
JF  - Engineering with Computers
N2  - The derivation of nonlocal strong forms for many physical problems remains cumbersome in traditional methods. In this paper, we apply the variational principle/weighted residual method based on nonlocal operator method for the derivation of nonlocal forms for elasticity, thin plate, gradient elasticity, electro-magneto-elasticity and phase-field fracture method. The nonlocal governing equations are expressed as an integral form on support and dual-support. The first example shows that the nonlocal elasticity has the same form as dual-horizon non-ordinary state-based peridynamics. The derivation is simple and general and it can convert efficiently many local physical models into their corresponding nonlocal forms. In addition, a criterion based on the instability of the nonlocal gradient is proposed for the fracture modelling in linear elasticity. Several numerical examples are presented to validate nonlocal elasticity and the nonlocal thin plate.
KW  - Bruchmechanik
KW  - Elastizität
KW  - Peridynamik
KW  - energy form
KW  - weak form
KW  - peridynamics
KW  - variational principle
KW  - explicit time integration
Y1  - 2021
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20211207-45388
UR  - https://link.springer.com/article/10.1007/s00366-021-01502-8
VL  - 2021
SP  - 1
EP  - 22
ER  -