The nonlocal theory solution of a Mode-I crack in functionally graded materials

Liang, Jun

doi:10.1007/s11431-008-0152-3

Cited by 5 publications

(3 citation statements)

References 33 publications

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“…A very extensive list of contributions is traceable in the relevant literature, see e.g. Eringen and Kim (1974) or Zhou and Wang (2005) till Liang (2009) just to quote one of the early contribution and a pair of the more recent ones. An effective nonlocal continuum approach for solving problems involving (spontaneous) formation of discontinuities, so including fracture mechanics problems, is the one known as peridynamic model proposed by Silling (2000); see also the recent contributions of Silling et al (2003) and Emmrich and Weckner (2007).…”

Section: Introductionmentioning

confidence: 99%

Nonlocal integral elasticity: 2D finite element based solutions

Pisano

Sofi

Fuschi

2009

International Journal of Solids and Structures

109

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a b s t r a c tA finite element based method, theorized in the context of nonlocal integral elasticity and founded on a nonlocal total potential energy principle, is numerically implemented for solving 2D nonlocal elastic problems. The key idea of the method, known as nonlocal finite element method (NL-FEM), relies on the assumption that the postulated nonlocal elastic behaviour of the material is captured by a finite element endowed with a set of (cross-stiffness) element's matrices able to interpret the (nonlocality) effects induced in the element itself by the other elements in the mesh. An Eringen-type nonlocal elastic model is assumed with a constitutive stress-strain law of convolutive-type which governs the nonlocal material behaviour. Computational issues, as the construction of the nonlocal element and global stiffness matrices, are treated in detail. Few examples are presented and the relevant numerical findings discussed both to verify the reliability of the method and to prove its effectiveness.

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Section: Introductionmentioning

confidence: 99%

Nonlocal integral elasticity: 2D finite element based solutions

Pisano

Sofi

Fuschi

2009

International Journal of Solids and Structures

109

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“…Huang et al [17] approached for crack propagation analysis in concrete structure by nonlocal peridynamic method. Liang [18] investigated behavior of mode-1 crack in functionally graded materials by non-local theory solutions and presented numerical examples of the effect of crack length.…”

Section: Introductionmentioning

confidence: 99%

Temperature and Strain Rate Dependent Mechanical Properties of a Square Nickel Plate with Different Shaped Central Cracks: A Molecular Dynamics Study

Gupta

Dutta

Shahadat

2018

JNanoR

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In our present study, under uniaxial tension, atomistic simulations were conducted to explore the crack propagation mechanism of Square Nickel Plate (SNP) for two distinct shaped cracks (Rectangular and Circular) at center separately. Here, for modeling the inter-atomic potential between atoms, Embedded Atom Model (EAM) was used. In case of both types, the crack size was varied keeping a constant strain rate of 2×109s-1and temperature of 300 k for investigation of the effects of crack geometry and size on the behavior of crack propagation. Along with the size and geometry of crack, the effects of different strain rates (1×109, 2×109and 4×109s-1) and temperatures (300 K, 600 K and 900 k) were also studied. From the simulations, the declination nature of peak stress can be deduced for both of the geometries by increasing the crack size. It can also be concluded that when crack area was same, the peak stresses were higher in SNP with Circular crack than with the SNP with Rectangular one. Besides, increasing and decreasing nature of peak stress were found for two genres with the increment of strain rate and temperature separately.

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“…[11][12][13][14][15]. The mechanical or thermal properties of nanostructures such as carbon nanotube, nanowire, nanoswitch, nanofilm, nanobeam, nanoplate, etc.…”

Section: Introductionmentioning

confidence: 99%

Transverse vibration of pre-tensioned nonlocal nanobeams with precise internal axial loads

Lim

et al. 2011

Sci. China Technol. Sci.

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This paper investigates the transverse vibration of a simply supported nanobeam with an initial axial tension based on the nonlocal stress field theory with a nonlocal size parameter. Considering an axial elongation due to transverse vibration, the internal axial tension is not precisely equal to the external initial tension. A sixth-order nonlinear partial differential equation that governs the transverse vibration for such nonlocal nanobeam is derived. Using a perturbation method, the relation between natural frequency and nonlocal nanoscale parameter is derived and the transverse vibration mode is solved. The external axial tension and nonlocal nanoscale parameter are proven to play significant roles in the nonlinear vibration behavior of nonlocal nanobeams. Such effects enhance the natural frequency and stiffness as compared to the predictions of the classical continuum mechanics models. Additionally, the frequency is higher if the precise internal axial load is considered with respect to that when only the approximate internal axial tension is assumed. nonlocal stress, natural frequency, free vibration, nonlocal nanoscale Citation:Li C, Lim C W, Yu J L, et al. Transverse vibration of pre-tensioned nonlocal nanobeams with precise internal axial loads.

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The nonlocal theory solution of a Mode-I crack in functionally graded materials

Cited by 5 publications

References 33 publications

Nonlocal integral elasticity: 2D finite element based solutions

Nonlocal integral elasticity: 2D finite element based solutions

Temperature and Strain Rate Dependent Mechanical Properties of a Square Nickel Plate with Different Shaped Central Cracks: A Molecular Dynamics Study

Transverse vibration of pre-tensioned nonlocal nanobeams with precise internal axial loads

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