Relevant bibliographies by topics / Gradient of elasticity

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  1. Journal articles

Academic literature on the topic 'Gradient of elasticity'

Author: Grafiati
Published: 24 June 2022

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Journal articles on the topic "Gradient of elasticity"

1

Askes, Harm, and Miguel A. Gutiérrez. "Implicit gradient elasticity." International Journal for Numerical Methods in Engineering 67, no. 3 (2006): 400–416. http://dx.doi.org/10.1002/nme.1640.

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2

Tarasov, Vasily E., and Elias C. Aifantis. "Toward fractional gradient elasticity." Journal of the Mechanical Behavior of Materials 23, no. 1-2 (2014): 41–46. http://dx.doi.org/10.1515/jmbm-2014-0006.

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AbstractThe use of an extension of gradient elasticity through the inclusion of spatial derivatives of fractional order to describe the power law type of non-locality is discussed. Two phenomenological possibilities are explored. The first is based on the Caputo fractional derivatives in one dimension. The second involves the Riesz fractional derivative in three dimensions. Explicit solutions of the corresponding fractional differential equations are obtained in both cases. In the first case, stress equilibrium in a Caputo elastic bar requires the existence of a nonzero internal body force to equilibrate it. In the second case, in a Riesz-type gradient elastic continuum under the action of a point load, the displacement may or may not be singular depending on the order of the fractional derivative assumed.
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3

Lurie, Sergey A., Alexander L. Kalamkarov, Yury O. Solyaev, and Alexander V. Volkov. "Dilatation gradient elasticity theory." European Journal of Mechanics - A/Solids 88 (July 2021): 104258. http://dx.doi.org/10.1016/j.euromechsol.2021.104258.

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4

Lazar, Markus. "On gradient field theories: gradient magnetostatics and gradient elasticity." Philosophical Magazine 94, no. 25 (2014): 2840–74. http://dx.doi.org/10.1080/14786435.2014.935512.

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5

Gutkin, M. Yu, and E. C. Aifantis. "Edge dislocation in gradient elasticity." Scripta Materialia 36, no. 1 (1997): 129–35. http://dx.doi.org/10.1016/s1359-6462(96)00352-1.

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6

Lazar, Markus, and Gérard A. Maugin. "Dislocations in gradient elasticity revisited." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2075 (2006): 3465–80. http://dx.doi.org/10.1098/rspa.2006.1699.

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In this paper, we consider dislocations in the framework of first as well as second gradient theory of elasticity. Using the Fourier transform, rigorous analytical solutions of the two-dimensional bi-Helmholtz and Helmholtz equations are derived in closed form for the displacement, elastic distortion, plastic distortion and dislocation density of screw and edge dislocations. In our framework, it was not necessary to use boundary conditions to fix constants of the solutions. The discontinuous parts of the displacement and plastic distortion are expressed in terms of two-dimensional as well as one-dimensional Fourier-type integrals. All other fields can be written in terms of modified Bessel functions.
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7

Hwang, K. C., T. F. Cuo, Y. Huang, and J. Y. Chen. "Fracture in strain gradient elasticity." Metals and Materials 4, no. 4 (1998): 593–600. http://dx.doi.org/10.1007/bf03026364.

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8

Gutkin, M. Yu, and E. C. Aifantis. "Screw dislocation in gradient elasticity." Scripta Materialia 35, no. 11 (1996): 1353–58. http://dx.doi.org/10.1016/1359-6462(96)00295-3.

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9

Giannakopoulos, Antonios E., Stylianos Petridis, and Dimitrios S. Sophianopoulos. "Dipolar gradient elasticity of cables." International Journal of Solids and Structures 49, no. 10 (2012): 1259–65. http://dx.doi.org/10.1016/j.ijsolstr.2012.02.008.

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10

Zervos, A. "Finite elements for elasticity with microstructure and gradient elasticity." International Journal for Numerical Methods in Engineering 73, no. 4 (2008): 564–95. http://dx.doi.org/10.1002/nme.2093.

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