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

2021 ◽  
Vol 384 ◽  
pp. 113963
Author(s):  
Huilong Ren ◽  
Xiaoying Zhuang ◽  
Nguyen-Thoi Trung ◽  
Timon Rabczuk
Keyword(s):  
Finite Deformation ◽  
Gradient Elasticity ◽  
Operator Method ◽  
Higher Order ◽  
Nonlocal Operator

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

2021 ◽  
Author(s):  
Huilong Ren ◽  
Xiaoying Zhuang ◽  
Erkan Oterkus ◽  
Hehua Zhu ◽  
Timon Rabczuk
Keyword(s):  
Thin Plate ◽  
Phase Field ◽  
Nonlocal Elasticity ◽  
Gradient Elasticity ◽  
Operator Method ◽  
Integral Form ◽  
Physical Models ◽  
Nonlocal Operator ◽  
Weighted Residual Method ◽  
Physical Problems

AbstractThe 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.

scholarly journals Implicit implementation of the nonlocal operator method: an open source code

2022 ◽  
Author(s):  
Yongzheng Zhang ◽  
Huilong Ren
Keyword(s):  
Open Source ◽  
Variational Principles ◽  
Source Code ◽  
Gradient Elasticity ◽  
Operator Method ◽  
Nonlinear Problems ◽  
Energy Functional ◽  
Benchmark Problems ◽  
Nonlocal Operator ◽  
Open Source Code

AbstractIn this paper, we present an open-source code for the first-order and higher-order nonlocal operator method (NOM) including a detailed description of the implementation. The NOM is based on so-called support, dual-support, nonlocal operators, and an operate energy functional ensuring stability. The nonlocal operator is a generalization of the conventional differential operators. Combined with the method of weighed residuals and variational principles, NOM establishes the residual and tangent stiffness matrix of operate energy functional through some simple matrix without the need of shape functions as in other classical computational methods such as FEM. NOM only requires the definition of the energy drastically simplifying its implementation. The implementation in this paper is focused on linear elastic solids for sake of conciseness through the NOM can handle more complex nonlinear problems. The NOM can be very flexible and efficient to solve partial differential equations (PDEs), it’s also quite easy for readers to use the NOM and extend it to solve other complicated physical phenomena described by one or a set of PDEs. Finally, we present some classical benchmark problems including the classical cantilever beam and plate-with-a-hole problem, and we also make an extension of this method to solve complicated problems including phase-field fracture modeling and gradient elasticity material.

Role of Higher-Order Elastic Moduli in Large Elastic Finite Deformation

1993 ◽  
Vol 32 (Part 1, No. 5B) ◽  
pp. 2252-2255
Author(s):  
Tetsuro Suzuki ◽  
Ken'ichi Osuka
Keyword(s):  
Finite Deformation ◽  
Elastic Moduli ◽  
Higher Order

Modeling the Tensile Size-Dependency in Polymer Nanofiber Elasticity

2011 ◽  
Vol 236-238 ◽  
pp. 2187-2190
Author(s):  
Bo Yuan ◽  
Qun Feng Liu ◽  
Cai Lin ◽  
Xiao Feng Chen
Keyword(s):  
Tensile Test ◽  
Model Prediction ◽  
Strain Gradient ◽  
Surface Effect ◽  
Gradient Elasticity ◽  
Tensile Tests ◽  
Higher Order ◽  
Uniaxial Tensile ◽  
Polymer Nanofiber ◽  
Strain Gradient Model

In this paper, a higher order strain gradient model is constructed to predict this size dependence of the elastic property of nanofibers under uniaxial tensile tests. We can show that the size effects in tensile test can be explained using a new model based on the higher order strain gradient elasticity (HSGE). A series of mechanical testing were performed to verify the model, and good agreement is found between the model prediction and the data obtained in the experiment. Compared with the model prediction based on surface effect (SE), our model can better capture the size effect in tensile test.

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