Preprints, Working Papers, ... Year : 2021

A nonlocal operator method for finite deformation higher-order gradient elasticity

Huilong Ren
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  • PersonId : 1089853
Nguyen-Thoi Trung
  • Function : Author
Timon Rabczuk
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  • PersonId : 955097

Abstract

We present a general finite deformation higher-order gradient elasticity theory. The governing equations of the higher-order gradient solid along with boundary conditions of various orders are derived from a variational principle using integration by parts on the surface. The objectivity of the energy functional is achieved by carefully selecting the invariants under rigid-body transformation. The third-order gradient solid theory includes more than 10.000 material parameters. However, under certain simplifications, the material parameters can be greatly reduced; down to 3. With this simplified formulation, we develop a nonlocal operator method and apply it to several numerical examples. The numerical analysis shows that the high gradient solid theory exhibits a stiffer response compared to a 'conventional' hyperelastic solid. The numerical tests also demonstrate the capability of the nonlocal operator method in solving higher-order physical problems.
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Dates and versions

hal-03127040 , version 1 (01-02-2021)
hal-03127040 , version 2 (31-05-2021)

Identifiers

  • HAL Id : hal-03127040 , version 2

Cite

Huilong Ren, Xiaoying Zhuang, Nguyen-Thoi Trung, Timon Rabczuk. A nonlocal operator method for finite deformation higher-order gradient elasticity. 2021. ⟨hal-03127040v2⟩
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