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Journal articles on the topic 'Gradient of elasticity'

Author: Grafiati

Published: 24 June 2022

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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

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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 o

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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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11

Mousavi, S. Mahmoud, Juha Paavola, and Djebar Baroudi. "Distributed non-singular dislocation technique for cracks in strain gradient elasticity." Journal of the Mechanical Behavior of Materials 23, no. 3-4 (2014): 47–58. http://dx.doi.org/10.1515/jmbm-2014-0007.

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AbstractThe mode III fracture analysis of a cracked graded plane in the framework of classical, first strain gradient, and second strain gradient elasticity is presented in this paper. Solutions to the problem of screw dislocation in graded materials are available in the literature. These solutions include various frameworks such as classical elasticity, and the first strain and second strain gradient elasticity theories. One of the applications of dislocations is the analysis of a cracked medium through distributed dislocation technique. In this article, this technique is used for the mode II

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12

Eremeyev, V. A., and F. dell’Isola. "Weak Solutions within the Gradient-Incomplete Strain-Gradient Elasticity." Lobachevskii Journal of Mathematics 41, no. 10 (2020): 1992–98. http://dx.doi.org/10.1134/s1995080220100078.

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13

Polizzotto, Castrenze. "Stress gradient versus strain gradient constitutive models within elasticity." International Journal of Solids and Structures 51, no. 9 (2014): 1809–18. http://dx.doi.org/10.1016/j.ijsolstr.2014.01.021.

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14

Efremidis,, G. T., and E. C. Aifantis,. "The Coefficient of Geostatic Stress: Gradient Elasticity vs. Classical Elasticity." Journal of the Mechanical Behavior of Materials 18, no. 1 (2007): 43–54. http://dx.doi.org/10.1515/jmbm.2007.18.1.43.

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15

Tarasov, Vasily E. "Fractional Gradient Elasticity from Spatial Dispersion Law." ISRN Condensed Matter Physics 2014 (April 3, 2014): 1–13. http://dx.doi.org/10.1155/2014/794097.

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Nonlocal elasticity models in continuum mechanics can be treated with two different approaches: the gradient elasticity models (weak nonlocality) and the integral nonlocal models (strong nonlocality). This paper focuses on the fractional generalization of gradient elasticity that allows us to describe a weak nonlocality of power-law type. We suggest a lattice model with spatial dispersion of power-law type as a microscopic model of fractional gradient elastic continuum. We demonstrate how the continuum limit transforms the equations for lattice with this spatial dispersion into the continuum e

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16

Lazar, Markus. "Incompatible strain gradient elasticity of Mindlin type: screw and edge dislocations." Acta Mechanica 232, no. 9 (2021): 3471–94. http://dx.doi.org/10.1007/s00707-021-02999-2.

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AbstractThe fundamental problem of dislocations in incompatible isotropic strain gradient elasticity theory of Mindlin type, unsolved for more than half a century, is solved in this work. Incompatible strain gradient elasticity of Mindlin type is the generalization of Mindlin’s compatible strain gradient elasticity including plastic fields providing in this way a proper eigenstrain framework for the study of defects like dislocations. Exact analytical solutions for the displacement fields, elastic distortions, Cauchy stresses, plastic distortions and dislocation densities of screw and edge dis

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17

Tarasov, Vasily E. "General lattice model of gradient elasticity." Modern Physics Letters B 28, no. 07 (2014): 1450054. http://dx.doi.org/10.1142/s0217984914500547.

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In this paper, new lattice model for the gradient elasticity is suggested. This lattice model gives a microstructural basis for second-order strain-gradient elasticity of continuum that is described by the linear elastic constitutive relation with the negative sign in front of the gradient. Moreover, the suggested lattice model allows us to have a unified description of gradient models with positive and negative signs of the strain gradient terms. Possible generalizations of this model for the high-order gradient elasticity and three-dimensional case are also suggested.

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18

Eremeyev, Victor A., Antonio Cazzani, and Francesco dell’Isola. "On nonlinear dilatational strain gradient elasticity." Continuum Mechanics and Thermodynamics 33, no. 4 (2021): 1429–63. http://dx.doi.org/10.1007/s00161-021-00993-6.

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AbstractWe call nonlinear dilatational strain gradient elasticity the theory in which the specific class of dilatational second gradient continua is considered: those whose deformation energy depends, in an objective way, on the gradient of placement and on the gradient of the determinant of the gradient of placement. It is an interesting particular case of complete Toupin–Mindlin nonlinear strain gradient elasticity: indeed, in it, the only second gradient effects are due to the inhomogeneous dilatation state of the considered deformable body. The dilatational second gradient continua are str

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19

Gusev, Andrei A., and Sergey A. Lurie. "Symmetry conditions in strain gradient elasticity." Mathematics and Mechanics of Solids 22, no. 4 (2015): 683–91. http://dx.doi.org/10.1177/1081286515606960.

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We study the variational significance of the “order-of-differentiation” symmetry condition of strain gradient elasticity. This symmetry condition stems from the fact that in strain gradient elasticity, one can interchange the order of differentiation in the components of the second displacement gradient tensor. We demonstrate that this symmetry condition is essential for the validity of free variational formulations commonly employed for deriving the field equations of strain gradient elasticity. We show that relying on this additional symmetry condition, one can restrict consideration to stra

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20

Volkov-Bogorodskii, D. B., and S. A. Lurie. "Eshelby integral formulas in gradient elasticity." Mechanics of Solids 45, no. 4 (2010): 648–56. http://dx.doi.org/10.3103/s0025654410040138.

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21

Tsagrakis, Ioannis, Igor S. Yasnikov, and Elias C. Aifantis. "Gradient elasticity for disclinated micro crystals." Mechanics Research Communications 93 (October 2018): 159–62. http://dx.doi.org/10.1016/j.mechrescom.2017.11.007.

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22

Konstantopoulos, Iason, and Elias Aifantis. "Gradient elasticity applied to a crack." Journal of the Mechanical Behavior of Materials 22, no. 5-6 (2013): 193–201. http://dx.doi.org/10.1515/jmbm-2013-0026.

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AbstractThe aim of this paper is to investigate the stress and the displacement field of a crack within a robust version of gradient elasticity, focusing at the standard Mode I, II, III problems. Special treatment is attributed to the crack configuration near its tip, deriving the gradient elasticity results that are analogous to the classical asymptotical solutions near the crack tip.

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23

Sun, Bohua, and E. C. Aifantis. "Gradient Elasticity Formulations for Micro/Nanoshells." Journal of Nanomaterials 2014 (2014): 1–4. http://dx.doi.org/10.1155/2014/846370.

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The focus of this paper is on illustrating how to extend the second author’s gradient theory of elasticity to shells. Three formulations are presented based on the implicit gradient elasticity constitutive relation1 -ld2∇2σij=Cijkl(1-ls2∇2)εkland its two approximations1+ls2∇2-ld2∇2σij=Cijklεklandσij=Cijkl(1+ld2∇2-ls2∇2)εkl.

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24

Gutkin, M. Yu, and E. C. Aifantis. "Dislocations and Disclinations in Gradient Elasticity." physica status solidi (b) 214, no. 2 (1999): 245–84. http://dx.doi.org/10.1002/(sici)1521-3951(199908)214:2<245::aid-pssb245>3.0.co;2-p.

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25

Fischer, Paul, Julia Mergheim та Paul Steinmann. "𝒞1 continuous discretization of gradient elasticity". PAMM 9, № 1 (2010): 435–36. http://dx.doi.org/10.1002/pamm.200910190.

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26

Lazopoulos, K. A., and A. K. Lazopoulos. "Strain gradient elasticity and stress fibers." Archive of Applied Mechanics 83, no. 9 (2013): 1371–81. http://dx.doi.org/10.1007/s00419-013-0752-7.

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27

Ma, Hansong, Gengkai Hu, Yueguang Wei, and Lihong Liang. "Inclusion problem in second gradient elasticity." International Journal of Engineering Science 132 (November 2018): 60–78. http://dx.doi.org/10.1016/j.ijengsci.2018.07.003.

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28

Fischer, Paul, Markus Klassen, Julia Mergheim, Paul Steinmann, and Ralf Müller. "Isogeometric analysis of 2D gradient elasticity." Computational Mechanics 47, no. 3 (2010): 325–34. http://dx.doi.org/10.1007/s00466-010-0543-8.

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29

Polizzotto, Castrenze. "Gradient elasticity and nonstandard boundary conditions." International Journal of Solids and Structures 40, no. 26 (2003): 7399–423. http://dx.doi.org/10.1016/j.ijsolstr.2003.06.001.

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30

Lazar, Markus, Gérard A. Maugin, and Elias C. Aifantis. "Dislocations in second strain gradient elasticity." International Journal of Solids and Structures 43, no. 6 (2006): 1787–817. http://dx.doi.org/10.1016/j.ijsolstr.2005.07.005.

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31

Papanicolopulos, S. A. "Chirality in isotropic linear gradient elasticity." International Journal of Solids and Structures 48, no. 5 (2011): 745–52. http://dx.doi.org/10.1016/j.ijsolstr.2010.11.007.

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32

Lazopoulos, K. A., and A. K. Lazopoulos. "Fractional derivatives and strain gradient elasticity." Acta Mechanica 227, no. 3 (2015): 823–35. http://dx.doi.org/10.1007/s00707-015-1489-x.

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33

Owen, David R. "Elasticity with Gradient-Disarrangements: A Multiscale Perspective for Strain-Gradient Theories of Elasticity and of Plasticity." Journal of Elasticity 127, no. 1 (2016): 115–50. http://dx.doi.org/10.1007/s10659-016-9599-9.

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34

XU, LIANG, and SHENGPING SHEN. "SIZE-DEPENDENT PIEZOELECTRICITY AND ELASTICITY DUE TO THE ELECTRIC FIELD-STRAIN GRADIENT COUPLING AND STRAIN GRADIENT ELASTICITY." International Journal of Applied Mechanics 05, no. 02 (2013): 1350015. http://dx.doi.org/10.1142/s1758825113500154.

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A size-dependent nonclassical Bernoulli–Euler beam model based on the strain gradient elasticity is proposed for piezoelectric nanowires. The governing equations and the corresponding boundary conditions are naturally derived from the variational principle. Different from the classical piezoelectric beam theory, the electric field–strain gradient coupling and the strain gradient elasticity are both taken into account. Static bending problem of a cantilever piezoelectric nanobeam is solved to illustrate the effect of strain gradient. The present model contains material length scale parameters a

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35

Lazar, Markus, and Giacomo Po. "On Mindlin’s isotropic strain gradient elasticity: Green tensors, regularization, and operator-split." Journal of Micromechanics and Molecular Physics 03, no. 03n04 (2018): 1840008. http://dx.doi.org/10.1142/s2424913018400088.

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The theory of Mindlin’s isotropic strain gradient elasticity of form II is reviewed. Three-dimensional and two-dimensional Green tensors and their first and second derivatives are derived for an unbounded medium. Using an operator-split in Mindlin’s strain gradient elasticity, three-dimensional and two-dimensional regularization function tensors are computed, which are the three-dimensional and two-dimensional Green tensors of a tensorial Helmholtz equation. In addition, a length scale tensor is introduced, which is responsible for the characteristic material lengths of strain gradient elastic

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36

Lazar, Markus. "Irreducible decomposition of strain gradient tensor in isotropic strain gradient elasticity." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 96, no. 11 (2016): 1291–305. http://dx.doi.org/10.1002/zamm.201500278.

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37

Aifantis, Elias C. "On scale invariance in anisotropic plasticity, gradient plasticity and gradient elasticity." International Journal of Engineering Science 47, no. 11-12 (2009): 1089–99. http://dx.doi.org/10.1016/j.ijengsci.2009.07.003.

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38

Peerlings, R. H. J., and N. A. Fleck. "Computational Evaluation of Strain Gradient Elasticity Constants." International Journal for Multiscale Computational Engineering 2, no. 4 (2004): 599–620. http://dx.doi.org/10.1615/intjmultcompeng.v2.i4.60.

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39

Solyaev, Yury, and Sergey A. Lurie. "ESHELBY INTEGRAL FORMULAS IN SECOND GRADIENT ELASTICITY." Nanoscience and Technology: An International Journal 11, no. 2 (2020): 99–107. http://dx.doi.org/10.1615/nanoscitechnolintj.2020031434.

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40

Carta, Giorgio, Terry Bennett, and Harm Askes. "Determination of dynamic gradient elasticity length scales." Proceedings of the Institution of Civil Engineers - Engineering and Computational Mechanics 165, no. 1 (2012): 41–47. http://dx.doi.org/10.1680/eacm.2012.165.1.41.

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41

Metrikine, A. V. "On causality of the gradient elasticity models." Journal of Sound and Vibration 297, no. 3-5 (2006): 727–42. http://dx.doi.org/10.1016/j.jsv.2006.04.017.

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42

Lazar, Markus. "Non-singular dislocation loops in gradient elasticity." Physics Letters A 376, no. 21 (2012): 1757–58. http://dx.doi.org/10.1016/j.physleta.2012.04.009.

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43

Gutkin, M. Yu, and E. C. Aifantis. "Dislocations in the theory of gradient elasticity." Scripta Materialia 40, no. 5 (1999): 559–66. http://dx.doi.org/10.1016/s1359-6462(98)00424-2.

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44

Gutkin, M. Yu, K. N. Mikaelyan, and E. C. Aifantis. "Screw dislocation near interface in gradient elasticity." Scripta Materialia 43, no. 6 (2000): 477–84. http://dx.doi.org/10.1016/s1359-6462(00)00445-0.

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45

Lam, D. C. C., F. Yang, A. C. M. Chong, J. Wang, and P. Tong. "Experiments and theory in strain gradient elasticity." Journal of the Mechanics and Physics of Solids 51, no. 8 (2003): 1477–508. http://dx.doi.org/10.1016/s0022-5096(03)00053-x.

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46

Auffray, N., H. Le Quang, and Q. C. He. "Matrix representations for 3D strain-gradient elasticity." Journal of the Mechanics and Physics of Solids 61, no. 5 (2013): 1202–23. http://dx.doi.org/10.1016/j.jmps.2013.01.003.

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47

Cordero, Nicolas M., Samuel Forest, and Esteban P. Busso. "Second strain gradient elasticity of nano-objects." Journal of the Mechanics and Physics of Solids 97 (December 2016): 92–124. http://dx.doi.org/10.1016/j.jmps.2015.07.012.

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48

Papanicolopulos, S. A., A. Zervos, and I. Vardoulakis. "A three-dimensionalC1finite element for gradient elasticity." International Journal for Numerical Methods in Engineering 77, no. 10 (2009): 1396–415. http://dx.doi.org/10.1002/nme.2449.

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49

Georgiadis, H. G., P. A. Gourgiotis, and D. S. Anagnostou. "The Boussinesq problem in dipolar gradient elasticity." Archive of Applied Mechanics 84, no. 9-11 (2014): 1373–91. http://dx.doi.org/10.1007/s00419-014-0854-x.

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50

Anagnostou, DS, PA Gourgiotis, and HG Georgiadis. "The Cerruti problem in dipolar gradient elasticity." Mathematics and Mechanics of Solids 20, no. 9 (2013): 1088–106. http://dx.doi.org/10.1177/1081286513514882.

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