Nonlinear Large Deformation of Graphene Sheets Using a Nonlocal-Based ANCF Method

A novel nonlinear model of single-layered graphene sheets (SLGSs) subject to large deformation is proposed using the absolute nodal coordinate formulation (ANCF) and the nonlocal elasticity theory. The geometrical definition of SLGSs is described by ANCF thin plate element while the strain energy is expressed by nonlocal theory. Then, the formulation of elastic force and the Jacobian of the elastic force is derived. We verify the proposed model by comparing the results with other published results and conduct corresponding numerical case study to clarify the influence of boundary conditions (BCs), nonlocal parameters, side length and aspect ratio. Large deformation problem of SLGSs with several BCs and different loading modes are simulated to study the mechanical nonlinearity of the SLGSs.

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Impact Dynamics of Single-Layered Graphene Sheets in Multibody Framework Using Nonlocal-Based-ANCF Modeling

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455419500998 ◽

2019 ◽

Vol 19 (09) ◽

pp. 1950099

Author(s):

Qingtao Wang ◽

Yang Zhang ◽

Qixin Zhu ◽

Zhaojun Pang

Keyword(s):

Pair Potential ◽

Gold Atom ◽

Nonlocal Elasticity Theory ◽

Nonlocal Theory ◽

Impact Dynamics ◽

Graphene Sheets ◽

Dynamic Simulations ◽

Definition Of ◽

Vdw Force ◽

The Impact

A new nonlinear model based on the absolute nodal coordinate formulation (ANCF) and the nonlocal elasticity theory is proposed to investigate the single-layered graphene sheets (SLGSs) impacted by nanoparticles. The geometrical definition of SLGSs is described by using the ANCF thin plate element, and the strain energy is expressed by using the nonlocal theory. The Lennard–Jones pair potential is adopted to model the van der Waals (vdW) force between SLGSs and nanoparticles. The impact dynamics of the system is simulated in multibody framework by using the generalized-alpha numerical integration method. The impact response of the gold atom–SLGSs system is simulated to validate the performance of the proposed model. Three impact dynamic simulations are conducted to investigate the influence of nanoparticles on the impact dynamics of SLGSs. The results show that the coupling of SLGSs vibration and vdW force led to the amplitude inconsistence of [Formula: see text]-position for nanoparticles.

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FEM Analysis on Three Dimensional Cutting. Analysis on Large Deformation Problem of Tool Entry.

Journal of the Japan Society for Precision Engineering ◽

10.2493/jjspe.59.1275 ◽

1993 ◽

Vol 59 (8) ◽

pp. 1275-1280 ◽

Cited By ~ 5

Author(s):

Hiroyuki SASAHARA ◽

Toshiyuki OBIKAWA ◽

Takahiro SHIRAKASHI

Keyword(s):

Large Deformation ◽

Three Dimensional ◽

Fem Analysis ◽

Deformation Problem ◽

Large Deformation Problem

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Description of Large Deformation Problem Using Means of Visual Strain

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.275-277.16 ◽

2013 ◽

Vol 275-277 ◽

pp. 16-22

Author(s):

You Liang Xu

Keyword(s):

Constitutive Equation ◽

Large Deformation ◽

Strain Tensor ◽

Visual Image ◽

Linear Strain ◽

Deformation Problem ◽

Practical Engineering ◽

Large Deformation Problem ◽

Strain Tensors ◽

Linear Strain Tensor

The constitutive equation of large deformation problem is closely related to geometric description. Nowadays, linear strain tensor is no longer unsuitable to describe large deformation. However, the existing non-linear strain tensors have complicated forms as well as no apparent geometric or physical meaning. While, the increment method is used to solve, however, convergence and efficiency are low sometimes. Thus the idea of visual strain tensor is proposed, with distinct meaning and visual image. Beside, it is likely to be used in engineering measurement, and it can be connected with measured constitutive equation directly. Thus this research provides a new idea and method for solving large-deformation problems in practical engineering.

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Large Deformation Problem of Bimodular Functionally-Graded Thin Circular Plates Subjected to Transversely Uniformly-Distributed Load: Perturbation Solution without Small-Rotation-Angle Assumption

Mathematics ◽

10.3390/math9182317 ◽

2021 ◽

Vol 9 (18) ◽

pp. 2317

Author(s):

Xue Li ◽

Xiao-Ting He ◽

Jie-Chuan Ai ◽

Jun-Yi Sun

Keyword(s):

Yield Stress ◽

Large Deformation ◽

Rotation Angle ◽

Functionally Graded ◽

Governing Equations ◽

Deformation Problem ◽

Distributed Load ◽

Large Deformation Problem ◽

Small Rotation ◽

Perturbation Solutions

In this study, the large deformation problem of a functionally-graded thin circular plate subjected to transversely uniformly-distributed load and with different moduli in tension and compression (bimodular property) is theoretically analyzed, in which the small-rotation-angle assumption, commonly used in the classical Föppl–von Kármán equations of large deflection problems, is abandoned. First, based on the mechanical model on the neutral layer, the bimodular functionally-graded property of materials is modeled as two different exponential functions in the tensile and compressive zones. Thus, the governing equations of the large deformation problem are established and improved, in which the equation of equilibrium is derived without the common small-rotation-angle assumption. Taking the central deflection as a perturbation parameter, the perturbation method is used to solve the governing equations, thus the perturbation solutions of deflection and stress are obtained under different boundary constraints and the regression of the solution is satisfied. Results indicate that the perturbation solutions presented in this study have higher computational accuracy in comparison with the existing perturbation solutions with small-rotation-angle assumption. Specially, the computational accuracies of external load and yield stress are improved by 17.22% and 28.79% at most, respectively, by the numerical examples. In addition, the small-rotation-angle assumption has a great influence on the yield stress at the center of the bimodular functionally-graded circular plate.

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