Multiscale coupling of molecular dynamics and peridynamics

Tong, Qi; Li, Shaofan

doi:10.1016/j.jmps.2016.05.032

Cited by 62 publications

(28 citation statements)

References 35 publications

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“…The timestep of explicit dynamic analysis is Δ t =1×10 −7 seconds for a duration of t =1×10 −4 seconds. An initial displacement with the shape of Gaussian distribution in polar coordinate is applied as

u false(r, t = 0 false) = ({, \begin{matrix} array A \exp - \frac{r^{2}}{2 r_{0}^{2}} (1 + b \cos \frac{4 π r}{r_{0}}), & array r \leq L_{c} \\ array 0, & array r > L_{c}, \end{matrix})

where A =0.0004, b =0.002, and r 0 =0.016 in meter. The truncation distance is given as L c =2 r 0 .…”

Section: Numerical Examplesmentioning

confidence: 99%

Voronoi‐based peridynamics and cracking analysis with adaptive refinement

Zhang

Xia

2017

Numerical Meth Engineering

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The most common technique for the numerical implementation of peridynamic theory is the uniform discretization together with constant horizon. However, unlike the nonuniform discretization and varying horizons, it is not a natural and intrinsic component of the adaptive refinement analysis and multiscale modeling. Besides, it encounters discretization difficulty in analyzing irregular structures. Therefore, to analyze problems with nonuniform discretization and varying horizons and solve the resulting problems of ghost forces and spurious wave reflection, the dual-horizon peridynamics based on uniform discretization is extended to the nonuniform discretization based on Voronoi diagrams, for which we call it Voronoi-based peridynamics. We redefine the damage definition as well. Next, an adaptive refinement analysis method based on the proposed Voronoi-based peridynamics and its numerical implementation is introduced. Finally, the traditional bond-based peridynamics and the Voronoi-based peridynamics with or without refinement are used to simulate 4 benchmark problems. The examples of 2-D quasi-static elastic deformation, 2-D wave propagation, 2-D dynamic crack growth, and 3-D simulation of the Kalthoff-Winkler experiment demonstrate the efficiency and effectivity of the proposed Voronoi-based peridynamics. Further, the adaptive refinement analysis can be used to obtain reasonable crack path and crack propagation speed with reduced computational burden.

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u false(r, t = 0 false) = ({, \begin{matrix} array A \exp - \frac{r^{2}}{2 r_{0}^{2}} (1 + b \cos \frac{4 π r}{r_{0}}), & array r \leq L_{c} \\ array 0, & array r > L_{c}, \end{matrix})

where A =0.0004, b =0.002, and r 0 =0.016 in meter. The truncation distance is given as L c =2 r 0 .…”

Section: Numerical Examplesmentioning

confidence: 99%

Voronoi‐based peridynamics and cracking analysis with adaptive refinement

Zhang

Xia

2017

Numerical Meth Engineering

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“…From this particular point of view, 500 × 500 material points for a test specimen is small in relation to the billions of atoms commonly simulated in molecular dynamics. The connection between peridynamics and molecular dynamics in fracture mechan-ics has been further discussed by Madenci and Oterkus (2014) and Tong and Li (2016).…”

Section: Resultsmentioning

confidence: 99%

The J-contour integral in peridynamics via displacements

Stenström

Eriksson

2019

Int J Fract

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Peridynamics is a nonlocal formulation of solid mechanics capable of unguided modelling of crack initiation, propagation and fracture. Peridynamics is based upon integral equations, thereby avoiding spatial derivatives, which are not defined at discontinuities, such as crack surfaces. Rice's J-contour integral is a firmly established expression in classic continuum solid mechanics, used as a fracture characterizing parameter for both linear and nonlinear elastic materials. A corresponding nonlocal J-integral has previously been derived for peridynamic modelling, which is based on the calculation of a set of displacement derivatives and force interactions associated with the contour of the integral. In this paper, we present an alternative calculation of the classical linear elastic J-integral for use in peridynamics, by writing Rice's J-integral as a function entirely of displacement derivatives. The accuracy of the proposed J-integral on displacement formulation is investigated by applying it to the exact analytical displacement solution of an infinite specimen with a central crack and comparing the exact analytical expression of its J-integral K 2 I /E. Further comparison with a well-known peridynamic crack problem shows very good agreement. The suggested method is computationally efficient and further allows testing of the accuracy of a peridynamic model as such.

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“…PD-FEM coupling is an approach aimed at taking advantage of both methods [79][80][81][82]. The interest in PD can also be understood from the coupling of PD with other formulations such as classical elasticity [83], poroelasticity [41,84], MD [85,86], finite point method [87] as well as damage models [88].…”

Section: General Coupling Techniquesmentioning

confidence: 99%

Peridynamics review

Javili

Morasata

Öterkuş

et al. 2018

Mathematics and Mechanics of Solids

239

109

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Peridynamics (PD) is a novel continuum mechanics theory established by Stewart Silling in 2000. The roots of PD can be traced back to the early works of Gabrio Piola according to dell’Isola et al. PD has been attractive to researchers as it is a non-local formulation in an integral form, unlike the local differential form of classical continuum mechanics. Although the method is still in its infancy, the literature on PD is fairly rich and extensive. The prolific growth in PD applications has led to a tremendous number of contributions in various disciplines. This manuscript aims to provide a concise description of the PD theory together with a review of its major applications and related studies in different fields to date. Moreover, we succinctly highlight some lines of research that are yet to be investigated.

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Multiscale coupling of molecular dynamics and peridynamics

Cited by 62 publications

References 35 publications

Voronoi‐based peridynamics and cracking analysis with adaptive refinement

Voronoi‐based peridynamics and cracking analysis with adaptive refinement

The J-contour integral in peridynamics via displacements

Peridynamics review

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