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Journal articles on the topic 'Non-linear elasticity'

Author: Grafiati

Published: 4 June 2021

Last updated: 19 April 2025

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1

Haughton, D. M. "On non-linear stability in unconstrained non-linear elasticity." International Journal of Non-Linear Mechanics 39, no. 7 (2004): 1181–92. http://dx.doi.org/10.1016/j.ijnonlinmec.2003.07.002.

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2

Mascolo, E., and L. Migliaccio. "Necking deformation in non-linear elasticity." Asymptotic Analysis 9, no. 2 (1994): 149–61. http://dx.doi.org/10.3233/asy-1994-9204.

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3

Guidorzi, M. "Partial regularity in non-linear elasticity." manuscripta mathematica 107, no. 1 (2002): 25–41. http://dx.doi.org/10.1007/s002290100221.

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4

Paroni, Roberto, та Giuseppe Tomassetti. "From non-linear elasticity to linear elasticity with initial stress via Γ-convergence". Continuum Mechanics and Thermodynamics 23, № 4 (2011): 347–61. http://dx.doi.org/10.1007/s00161-011-0184-y.

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5

Droniou, Jérôme, and Bishnu P. Lamichhane. "Gradient schemes for linear and non-linear elasticity equations." Numerische Mathematik 129, no. 2 (2014): 251–77. http://dx.doi.org/10.1007/s00211-014-0636-y.

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6

Jelenić, Gordan. "Pure bending in non-linear micropolar elasticity." International Journal of Mechanics and Materials in Design 18, no. 1 (2021): 243–65. http://dx.doi.org/10.1007/s10999-021-09577-3.

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7

Mazilu, P. "Variational Principles in Heterogeneous Non-Linear Elasticity." Materials Science Forum 123-125 (January 1993): 185–94. http://dx.doi.org/10.4028/www.scientific.net/msf.123-125.185.

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8

Ricker, M., and H.-R. Trebin. "Non-linear generalized elasticity of icosahedral quasicrystals." Journal of Physics A: Mathematical and General 35, no. 32 (2002): 6953–62. http://dx.doi.org/10.1088/0305-4470/35/32/314.

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9

Bataille, Klaus, and Ignacia Calisto. "Seismic coda due to non-linear elasticity." Geophysical Journal International 172, no. 2 (2008): 572–80. http://dx.doi.org/10.1111/j.1365-246x.2007.03639.x.

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10

Gersborg, Allan R., and Ole Sigmund. "Extreme non-linear elasticity and transformation optics." Optics Express 18, no. 18 (2010): 19020. http://dx.doi.org/10.1364/oe.18.019020.

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11

Chaudhuri, O., S. Parekh, and D. A. Fletcher. "Non-linear elasticity of growing actin networks." Journal of Biomechanics 39 (January 2006): S235. http://dx.doi.org/10.1016/s0021-9290(06)83875-3.

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12

Rajagopal, K. R., and A. S. Wineman. "New exact solutions in non-linear elasticity." International Journal of Engineering Science 23, no. 2 (1985): 217–34. http://dx.doi.org/10.1016/0020-7225(85)90076-x.

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13

Ten Eyck, A., and A. Lew. "Discontinuous Galerkin methods for non-linear elasticity." International Journal for Numerical Methods in Engineering 67, no. 9 (2006): 1204–43. http://dx.doi.org/10.1002/nme.1667.

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14

Picard, Rainer. "Linear thermo-elasticity in non-smooth media." Mathematical Methods in the Applied Sciences 28, no. 18 (2005): 2183–99. http://dx.doi.org/10.1002/mma.657.

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15

Pideri, C., and P. Seppecher. "Asymptotics of a non-planar rod in non-linear elasticity." Asymptotic Analysis 48, no. 1-2 (2006): 33–54. https://doi.org/10.3233/asy-2006-761.

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We study the asymptotic behavior of a non-linear elastic material lying in a thin neighborhood of a non-planar line when the diameter of the section tends to zero. We first estimate the rigidity constant in such a domain then we prove the convergence of the three-dimensional model to a one-dimensional model. This convergence is established in the framework of $\varGamma $ -convergence. The resulting model is the one classically used in mechanics. It corresponds to a non-extensional line subjected to flexion and torsion. The torsion is an internal parameter which can eventually by eliminated but this elimination leads to a non-local energy. Indeed the non-planar geometry of the line couples the flexion and torsion terms.

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16

Checco, A. "Non-linear elasticity of a liquid contact line." EPL (Europhysics Letters) 85, no. 1 (2009): 16002. http://dx.doi.org/10.1209/0295-5075/85/16002.

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17

Apostol, B. F. "On a non-linear wave equation in elasticity." Physics Letters A 318, no. 6 (2003): 545–52. http://dx.doi.org/10.1016/j.physleta.2003.09.064.

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18

Bosher, S. H. B., and D. J. Dunstan. "PRACTICAL NON-LINEAR ELASTICITY THEORY FOR LARGE STRAINS." High Pressure Research 23, no. 3 (2003): 323–27. http://dx.doi.org/10.1080/0895795031000139208.

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19

Elżanowski, M., and M. Epstein. "Decay of strong shocks in non-linear elasticity." Journal of Sound and Vibration 103, no. 3 (1985): 371–78. http://dx.doi.org/10.1016/0022-460x(85)90429-8.

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20

Titarev, V. A., E. Romenski, and E. F. Toro. "MUSTA-type upwind fluxes for non-linear elasticity." International Journal for Numerical Methods in Engineering 73, no. 7 (2008): 897–926. http://dx.doi.org/10.1002/nme.2096.

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21

Edman, K. A. P. "Non-linear myofilament elasticity in frog intact muscle fibres." Journal of Experimental Biology 212, no. 8 (2009): 1115–19. http://dx.doi.org/10.1242/jeb.020982.

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22

Picinbono, Guillaume, Hervé Delingette, and Nicholas Ayache. "Non-linear anisotropic elasticity for real-time surgery simulation." Graphical Models 65, no. 5 (2003): 305–21. http://dx.doi.org/10.1016/s1524-0703(03)00045-6.

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23

Pitteri, M. "Some problems in non-linear elasticity of crystalline solids." Continuum Mechanics and Thermodynamics 2, no. 2 (1990): 99–117. http://dx.doi.org/10.1007/bf01126717.

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24

Brun, M., D. Capuani, and D. Bigoni. "A boundary element technique for incremental, non-linear elasticity." Computer Methods in Applied Mechanics and Engineering 192, no. 22-24 (2003): 2461–79. http://dx.doi.org/10.1016/s0045-7825(03)00268-8.

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25

Brun, M., D. Bigoni, and D. Capuani. "A boundary element technique for incremental, non-linear elasticity." Computer Methods in Applied Mechanics and Engineering 192, no. 22-24 (2003): 2481–99. http://dx.doi.org/10.1016/s0045-7825(03)00272-x.

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26

Lu, J., and P. Papadopoulos. "A covariant constitutive description of anisotropic non-linear elasticity." Zeitschrift für angewandte Mathematik und Physik 51, no. 2 (2000): 204. http://dx.doi.org/10.1007/s000330050195.

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27

Azarov, Daniil Anatolievich, and Leonid Mikhailovich Zubov. "Mechanical-Geometrical Modelling in Non-Linear Theory of Elasticity." UNIVERSITY NEWS. NORTH-CAUCASIAN REGION. NATURAL SCIENCES SERIES, no. 3 (2016): 5–12. http://dx.doi.org/10.18522/0321-3005-2016-3-5-12.

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28

Weckner, Olaf, Gerd Brunk, Michael A. Epton, Stewart A. Silling, and Ebrahim Askari. "Green’s functions in non-local three-dimensional linear elasticity." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2111 (2009): 3463–87. http://dx.doi.org/10.1098/rspa.2009.0234.

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In this paper, we compare small deformations in an infinite linear elastic body due to the presence of point loads within the classical, local formulation to the corresponding deformations in the peridynamic, non-local formulation. Owing to the linearity of the problem, the response to a point load can be used to obtain the response to general body force loading functions by superposition. Using Laplace and Fourier transforms, we thus obtain an integral representation for the three-dimensional peridynamic solution with the help of Green’s functions. We illustrate this new theoretical result by dynamic and static examples in one and three dimensions. In addition to this main result, we also derive the non-local three-dimensional jump conditions, as well as the weak formulation of peridynamics together with the associated finite element discretization.

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29

Temizer, I., and T. I. Zohdi. "A numerical method for homogenization in non-linear elasticity." Computational Mechanics 40, no. 2 (2006): 281–98. http://dx.doi.org/10.1007/s00466-006-0097-y.

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30

Kabaria, Hardik, Adrian J. Lew, and Bernardo Cockburn. "A hybridizable discontinuous Galerkin formulation for non-linear elasticity." Computer Methods in Applied Mechanics and Engineering 283 (January 2015): 303–29. http://dx.doi.org/10.1016/j.cma.2014.08.012.

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31

Faghidian, S. Ali. "On non-linear flexure of beams based on non-local elasticity theory." International Journal of Engineering Science 124 (March 2018): 49–63. http://dx.doi.org/10.1016/j.ijengsci.2017.12.002.

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32

Goswami, Soumya, Rifat Ahmed, Siladitya Khan, Marvin M. Doyley, and Stephen A. McAleavey. "Shear Induced Non-Linear Elasticity Imaging: Elastography for Compound Deformations." IEEE Transactions on Medical Imaging 39, no. 11 (2020): 3559–70. http://dx.doi.org/10.1109/tmi.2020.2999439.

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33

Calisto, Ignacia, Klaus Bataille, Manfred Stiller, and James Mechie. "Evidence that non-linear elasticity contributes to the seismic coda." Geophysical Journal International 180, no. 3 (2010): 1353–58. http://dx.doi.org/10.1111/j.1365-246x.2009.04492.x.

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34

Caraballo, Tomás, and Renato Colucci. "Pullback attractor for a non-linear evolution equation in elasticity." Nonlinear Analysis: Real World Applications 15 (January 2014): 80–88. http://dx.doi.org/10.1016/j.nonrwa.2013.06.002.

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35

Federico, Salvatore. "Covariant formulation of the tensor algebra of non-linear elasticity." International Journal of Non-Linear Mechanics 47, no. 2 (2012): 273–84. http://dx.doi.org/10.1016/j.ijnonlinmec.2011.06.007.

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36

Molenkamp, F. "Simple model for isotropic non-linear elasticity of frictional materials." International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts 26, no. 2 (1989): 76. http://dx.doi.org/10.1016/0148-9062(89)90210-6.

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37

Freddi, Francesco, and Gianni Royer-Carfagni. "From Non-Linear Elasticity to Linearized Theory: Examples Defying Intuition." Journal of Elasticity 96, no. 1 (2009): 1–26. http://dx.doi.org/10.1007/s10659-009-9191-7.

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38

Lee, Sungro, and Hyo-Sun Kim. "Time-Varying Income Elasticity of CO2emission Using Non-Linear Cointegration." Environmental and Resource Economics Review 23, no. 3 (2014): 473–96. http://dx.doi.org/10.15266/kerea.2014.23.3.473.

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39

Emeriault, F., and B. Cambou. "Micromechanical modelling of anisotropic non-linear elasticity of granular medium." International Journal of Solids and Structures 33, no. 18 (1996): 2591–607. http://dx.doi.org/10.1016/0020-7683(95)00170-0.

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40

Whiteley, Jonathan P. "Discontinuous Galerkin finite element methods for incompressible non-linear elasticity." Computer Methods in Applied Mechanics and Engineering 198, no. 41-44 (2009): 3464–78. http://dx.doi.org/10.1016/j.cma.2009.07.002.

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41

Oquendo, Higidio Portillo. "A transmission problem with non-linear internal damping in elasticity." Mathematical Methods in the Applied Sciences 26, no. 10 (2003): 815–30. http://dx.doi.org/10.1002/mma.365.

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42

Goleniewski, G. "Low-order mixed method finite elements in non-linear elasticity." Communications in Applied Numerical Methods 7, no. 1 (1991): 57–63. http://dx.doi.org/10.1002/cnm.1630070109.

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43

Hueckel, T., E. Tutumluer, and R. Pellegrini. "A note on non-linear elasticity of isotropic overconsolidated clays." International Journal for Numerical and Analytical Methods in Geomechanics 16, no. 8 (1992): 603–18. http://dx.doi.org/10.1002/nag.1610160805.

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44

Bufler, H. "A Unified Representation of Variational Principles in Non-Linear Elasticity." ZAMM 80, no. 1 (2000): 53–59. http://dx.doi.org/10.1002/(sici)1521-4001(200001)80:1<53::aid-zamm53>3.0.co;2-4.

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45

LeVeque, Randall J. "Finite-volume methods for non-linear elasticity in heterogeneous media." International Journal for Numerical Methods in Fluids 40, no. 1-2 (2002): 93–104. http://dx.doi.org/10.1002/fld.309.

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46

Atlaoui, D., A. Mansouri, and H. Ait Aider. "Prediction of the Non-Linear Rupture of a Section Under Compound Deviated Bending." Journal of Applied Engineering Sciences 14, no. 1 (2024): 11–16. http://dx.doi.org/10.2478/jaes-2024-0002.

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Abstract Under stresses close to the ultimate stresses, a reinforced concrete section yields and cracks. The calculation in linear elasticity no longer makes it possible to evaluate the real deformations of the section. One is then led to make a study in nonlinear elasticity. The object of this work is the elaboration of a calculation method in nonlinear elasticity, allowing the simulation until the failure of reinforced concrete sections subjected to a compound deviated bending taking into account the real behavior laws (nonlinear) of the materials (steel and concrete). A computer program is developed following FORTRAN standards, and then confronted with the obtained experimental results on failure tests of sections subjected to deflected bending. The comparison between the numerical simulation and the experimental test/calculation shows the achievement of satisfactory results.

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47

Poryles, Raphaël, Théo Lenavetier, Emmanuel Schaub, Adrien Bussonnière, Arnaud Saint-Jalmes, and Isabelle Cantat. "Non linear elasticity of foam films made of SDS/dodecanol mixtures." Soft Matter 18, no. 10 (2022): 2046–53. http://dx.doi.org/10.1039/d1sm01733k.

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48

Roos, Alexandra, and Costantino Creton. "Linear Viscoelasticity and Non-Linear Elasticity of Block Copolymer Blends Used as Soft Adhesives." Macromolecular Symposia 214, no. 1 (2004): 147–56. http://dx.doi.org/10.1002/masy.200451011.

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49

Whiteley, Jonathan P. "The Solution of Inverse Non-Linear Elasticity Problems That Arise When Locating Breast Tumours." Journal of Theoretical Medicine 6, no. 3 (2005): 143–49. http://dx.doi.org/10.1080/10273660500148606.

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Non-linear elasticity theory may be used to calculate the coordinates of a deformed body when the coordinates of the undeformed, stress-free body are known. In some situations, such as one of the steps in the location of tumours in a breast, the coordinates of the deformed body are known and the coordinates of the undeformed body are to be calculated, i.e. we require the solution of the inverse problem. Other than for situations where classical linear elasticity theory may be applied, the simple approach for solving the inverse problem of reversing the direction of gravity and modelling the deformed body as an undeformed body does not give the correct solution. In this study, we derive equations that may be used to solve inverse problems. The solution of these equations may be used for a wide range of inverse problems in non-linear elasticity.

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50

Adjrad, Arezki, Youcef Bouafia, Mohand Said Kachi, and Hélène Dumontet. "Modeling of Externally Prestressed Beams until Fracture in Non Linear Elasticity." Applied Mechanics and Materials 749 (April 2015): 379–85. http://dx.doi.org/10.4028/www.scientific.net/amm.749.379.

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In this paper, we present an analytical model to analyze reinforced and prestressed concrete beams loaded in combined bending, axial load and shear, in the frame of non linear elasticity. In this model, the equilibrium of the beam is expressed by solving a system of equations, governing beams equilibrium, based on the stiffness matrix of the beam, which connects the load vector to the node displacements vector of the beam. It is built from the stiffness matrix of the section which takes into account a variation of the shearing modulus (depending on the shear variation) instead of assuming a constant shearing modulus as in linear elasticity. For the internal tendons, the stiffness matrix is completed by the terms due to the prestress effect in flexural equilibrium and by the balancing of one part of the shear by the transverse component of the force in the inclined cables.

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