Nonlocal strong forms of thin plate, gradient elasticity, magneto-electro-elasticity and phase field fracture by nonlocal operator method

Huilong Ren, Xiaoying Zhuang, Erkan Oterkus, Hehua Zhu, Timon Rabczuk

Research output: Contribution to journalArticlepeer-review

Abstract

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 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.
Original languageEnglish
Number of pages44
JournalEngineering with Computers
Publication statusAccepted/In press - 12 Aug 2021

Keywords

  • energy form
  • weak form
  • variational principle
  • peridynamics
  • dual-support
  • fracture
  • explicit time integration

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