Bridging scale simulation of lattice fracture using enriched space‐time Finite Element Method

Qian, Dong; Chirputkar, Shardool

doi:10.1002/nme.4610

Cited by 15 publications

(4 citation statements)

References 55 publications

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“…buckling region, and the coarse scale description became inaccurate. In such cases, the multiscale atomistic/continuum approach, such as those developed previously by the authors [36,[51][52][53] and others [54][55][56][57], shall be further explored.…”

Section: Compression Of a Five-layered Graphene Sheetmentioning

confidence: 99%

“…This is mainly due to the fact that the fine scale features of MM model were not well described by the coarse scale SS model in the buckling region, and the coarse scale description became inaccurate. In such cases, the multiscale atomistic/continuum approach, such as those developed previously by the authors and others , shall be further explored.…”

Section: Benchmark Examplesmentioning

confidence: 99%

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Coarse‐grained modeling and simulation of graphene sheets based on a discrete hyperelastic approach

Qian

Zhou

Zheng

2015

Numerical Meth Engineering

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SUMMARYA discrete hyperelastic model was developed in this paper for a single atomic layer of graphene structure that was originally planar. This model can be viewed as an extension to the well-known continuum hyperelastic model. Based on the discrete nature of the atomic structure, the notion of discrete mapping and the concept of spatial secant were introduced. The spatial secant served as a deformation measure that provided a geometric exact mapping in the discrete sense between the atomistic and continuum representations. By incorporating a physics-based interatomic potential, the corresponding discrete hyperelastic model was then established. After an introduction of the model, the computational implementation using the Galerkin finite element and/or meshfree method was outlined. The computational framework was then applied to study of the mechanics of graphene sheets. Extensive comparisons with full-scale molecular mechanics simulations and experimental measurement were made to illustrate the robustness of this approach.

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Section: Compression Of a Five-layered Graphene Sheetmentioning

confidence: 99%

Section: Benchmark Examplesmentioning

confidence: 99%

Coarse‐grained modeling and simulation of graphene sheets based on a discrete hyperelastic approach

Qian

Zhou

Zheng

2015

Numerical Meth Engineering

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“…An elaborate interfacial region is usually set for seamless coupling. Typical concurrent multiscale methods include finite‐element and atomic method, 6 atomistic/dislocation/continuum coupling method, 7 quasi‐continuum method, 8,9 bridging scale method, 10‐13 bridging domain method, 14,15 atomic‐to‐continuum blending method, 16,17 coupling of length scales method 18 . In the far‐field region, the finite element method, 6,7 the smoothed particle hydrodynamics (SPH) method, 19 the reproducing kernel particle method (RKPM), 11 the meshless local Petrov‐Galerkin (MLPG) method, 20 the material point method (MPM) 21,22 , the peridynamics method (PD), 23 and the dissipative particle dynamics/smoothed dissipative particle dynamics (DPD/SDPD) method 24,25 have been used.…”

Section: Introductionmentioning

confidence: 99%

An improved smoothed molecular dynamics method with high‐order shape function

Shuai

Zhao

Liu

2021

Numerical Meth Engineering

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As an efficient molecular simulation method, the smoothed molecular dynamics (SMD) method introduces background mesh and mapping process into molecular dynamics (MD) procedure to suppress high‐frequency modes, so that a much larger time step than that of MD can be adopted. SMD method can achieve a nice overall accuracy, but local atomic disorders cannot be described very well with original SMD method for smoothing out high‐frequency motions. An improved SMD method with two kinds of high‐order shape functions is proposed. A parameter indicating the smoothing degree in SMD method is also presented to assess the mapping process. The efficiency and the accuracy of the improved method are discussed in detail, and the proposed method is validated with several examples. The results demonstrate obvious improvement in accuracy, and more high‐frequency atomic motions can be captured. When the high‐order SMD method is coupled with the MD method, the non‐physical phonon reflection, which may occur at the interface in the coupling of MD and original SMD method, will decrease remarkably even if no transition scheme is employed.

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“…Recent years witnessed fast development of concurrent multiscale methods. Typical concurrent multiscale methods include the coupled atomic and discrete dislocation method , the heterogeneous multiscale method , the bridging scale method , the bridging domain method , blending the stress and the atomic force , combination of the solution processes of MD and FEM , and the coupling method of space‐time finite element and MD . Literatures reviewed concurrent multiscale methods in detail.…”

Section: Introductionmentioning

confidence: 99%

Seamless coupling of molecular dynamics and material point method via smoothed molecular dynamics

Liu

Zhang

2017

Int. J. Numer. Meth. Engng

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A concurrent multiscale method coupling molecular dynamics (MD) and continuum-based material point method (MPM) is proposed. Seamless coupling is realized by utilizing smoothed molecular dynamics (SMD) method. One set of background mesh is used in SMD method. Atomic equations of motion are assembled onto mesh nodes, and atomic variables are updated with nodal increments. SMD allows much larger time step size than MD critical time step size but keeps nice global accuracy. SMD is similar to MD except for the mapping process between background mesh nodes and atoms. SMD and MPM share the feature using the background mesh to solve momentum equations and to update variables. So bridging MD and MPM via SMD is straightforward and concise. A recently proposed transition scheme based on frequency decomposition is adopted to suppress phonon reflection at MD-SMD interface. The nodal equations in SMD-MPM interface region have contributions from both atoms and material points, which ensure the consistency between SMD region and MPM region. A multiple-time-step scheme is adopted for high efficiency. Numerical examples including wave propagation, bending, and crack propagation validate the proposed method, and the results show nice accuracy. The computational cost is greatly saved compared with pure MD computation. Copyright 381 multiscale method [7], the bridging scale method [8], the bridging domain method [9], blending the stress and the atomic force [10], combination of the solution processes of MD and FEM [11], and the coupling method of space-time finite element and MD [12]. Literatures [1,2,13] reviewed concurrent multiscale methods in detail.The major issue in developing accurate concurrent multiscale methods is seamless transition between atomic regions and continuum regions. Inconsistent description of the high-frequency waves may arouse the reflection at the interface of the atomic region and the continuum region. Wagner and Liu [8] proposed a bridging scale method, where a convolution is evaluated at the interface to absorb potential phonon reflection. Xiao and Belytschko [9] proposed to use the Lagrange multiplier method or the augmented Lagrange multiplier method to ensure seamless transition. The method was named the bridging domain method. To and Li [14] presented a perfectly matched layer method by enforcing the impedance matching at the interface. A blending scheme satisfying Newton's third law and leading to symmetric formulation was carefully designed by Badia et al. [15]. Wang and Tang [16] proposed an absorbing scheme by enforcing the dispersion condition while involving a minimal number of atoms. How to reduce the heavy computational cost of interface treatment while reserving high accuracy is still the focus of multiscale methods. He et al. [17] recently proposed an efficient and accurate transition scheme on the basis of frequency decomposition.Coarse-graining simulation is another promising way to effectively reduce the huge number of atomic degrees of freedom. Rudd and Broughton proposed the coarse-g...

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Bridging scale simulation of lattice fracture using enriched space‐time Finite Element Method

Cited by 15 publications

References 55 publications

Coarse‐grained modeling and simulation of graphene sheets based on a discrete hyperelastic approach

Coarse‐grained modeling and simulation of graphene sheets based on a discrete hyperelastic approach

An improved smoothed molecular dynamics method with high‐order shape function

Seamless coupling of molecular dynamics and material point method via smoothed molecular dynamics

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