Details
| Original language | English |
|---|---|
| Article number | 113963 |
| Journal | Computer Methods in Applied Mechanics and Engineering |
| Volume | 384 |
| Early online date | 16 Jun 2021 |
| Publication status | Published - 1 Oct 2021 |
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.
Keywords
- Finite strain, Invariant, Nonlocal operator method, Second/third-gradient strain, Variational principle
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Physics and Astronomy(all)
- Computer Science(all)
- Computer Science Applications
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In: Computer Methods in Applied Mechanics and Engineering, Vol. 384, 113963, 01.10.2021.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A nonlocal operator method for finite deformation higher-order gradient elasticity
AU - Ren, Huilong
AU - Zhuang, Xiaoying
AU - Trung, Nguyen Thoi
AU - Rabczuk, Timon
PY - 2021/10/1
Y1 - 2021/10/1
N2 - 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.
AB - 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.
KW - Finite strain
KW - Invariant
KW - Nonlocal operator method
KW - Second/third-gradient strain
KW - Variational principle
UR - http://www.scopus.com/inward/record.url?scp=85108005063&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2021.113963
DO - 10.1016/j.cma.2021.113963
M3 - Article
AN - SCOPUS:85108005063
VL - 384
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
SN - 0045-7825
M1 - 113963
ER -