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Статті в журналах з теми "Linearized Elasticity"

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Автор: Grafiati

Опубліковано: 10 грудня 2022

Оновлено: 9 березня 2023

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1

Slaughter, WS, and J. Petrolito. "Linearized Theory of Elasticity." Applied Mechanics Reviews 55, no. 5 (September 1, 2002): B90—B91. http://dx.doi.org/10.1115/1.1497478.

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2

Yavari, Arash, and Arkadas Ozakin. "Covariance in linearized elasticity." Zeitschrift für angewandte Mathematik und Physik 59, no. 6 (March 26, 2008): 1081–110. http://dx.doi.org/10.1007/s00033-007-7127-2.

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3

Bociu, Lorena, Steven Derochers, and Daniel Toundykov. "Linearized hydro-elasticity: A numerical study." Evolution Equations and Control Theory 5, no. 4 (October 2016): 533–59. http://dx.doi.org/10.3934/eect.2016018.

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4

CIARLET, PHILIPPE G., PATRICK CIARLET, OANA IOSIFESCU, STEFAN SAUTER, and JUN ZOU. "LAGRANGE MULTIPLIERS IN INTRINSIC ELASTICITY." Mathematical Models and Methods in Applied Sciences 21, no. 04 (April 2011): 651–66. http://dx.doi.org/10.1142/s0218202511005167.

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Анотація:

In an intrinsic approach to three-dimensional linearized elasticity, the unknown is the linearized strain tensor field (or equivalently the stress tensor field by means of the constitutive equation), instead of the displacement vector field in the classical approach. We consider here the pure traction problem and the pure displacement problem and we show that, in each case, the intrinsic approach leads to a quadratic minimization problem constrained by Donati-like relations (the form of which depends on the type of boundary conditions considered). Using the Babuška-Brezzi inf-sup condition, we then show that, in each case, the minimizer of the constrained minimization problem found in an intrinsic approach is the first argument of the saddle-point of an ad hoc Lagrangian, so that the second argument of this saddle-point is the Lagrange multiplier associated with the corresponding constraints. Such results have potential applications to the numerical analysis and simulation of the intrinsic approach to three-dimensional linearized elasticity.

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5

Ciarlet, Philippe G., and Cristinel Mardare. "Intrinsic formulation of the displacement-traction problem in linearized elasticity." Mathematical Models and Methods in Applied Sciences 24, no. 06 (March 28, 2014): 1197–216. http://dx.doi.org/10.1142/s0218202513500814.

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Анотація:

The displacement-traction problem of linearized elasticity is a system of partial differential equations and boundary conditions whose unknown is the displacement field inside a linearly elastic body. We explicitly identify here the corresponding boundary conditions satisfied by the linearized strain tensor field associated with such a displacement field. Using this identification, we are then able to provide an intrinsic formulation of the displacement-traction problem of linearized elasticity, by showing how it can be recast into a boundary value problem whose unknown is the linearized strain tensor field.

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6

Friedrich, Manuel, and Francesco Solombrino. "Quasistatic crack growth in 2d-linearized elasticity." Annales de l'Institut Henri Poincaré C, Analyse non linéaire 35, no. 1 (January 2018): 27–64. http://dx.doi.org/10.1016/j.anihpc.2017.03.002.

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7

Ciarlet, Philippe G., Patrick Ciarlet, Oana Iosifescu, Stefan Sauter, and Jun Zou. "A Lagrangian approach to intrinsic linearized elasticity." Comptes Rendus Mathematique 348, no. 9-10 (May 2010): 587–92. http://dx.doi.org/10.1016/j.crma.2010.04.011.

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8

Serrano, Hélia. "Homogenization of kinetic laminates in linearized elasticity." Mathematical Methods in the Applied Sciences 41, no. 1 (October 5, 2017): 270–80. http://dx.doi.org/10.1002/mma.4611.

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9

Gussmann, Pascal, and Alexander Mielke. "Linearized elasticity as Mosco limit of finite elasticity in the presence of cracks." Advances in Calculus of Variations 13, no. 1 (January 1, 2020): 33–52. http://dx.doi.org/10.1515/acv-2017-0010.

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AbstractThe small-deformation limit of finite elasticity is considered in presence of a given crack. The rescaled finite energies with the constraint of global injectivity are shown to Γ-converge to the linearized elastic energy with a local constraint of non-interpenetration along the crack.

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10

Carlson, Donald E. "On the range of applicability of linearized elasticity." Mathematics and Mechanics of Solids 16, no. 5 (April 13, 2011): 467–81. http://dx.doi.org/10.1177/1081286510387527.

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11

CIARLET, PHILIPPE G., and PATRICK CIARLET. "DIRECT COMPUTATION OF STRESSES IN PLANAR LINEARIZED ELASTICITY." Mathematical Models and Methods in Applied Sciences 19, no. 07 (July 2009): 1043–64. http://dx.doi.org/10.1142/s0218202509003711.

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Анотація:

Given a simply-connected domain Ω in ℝ2, consider a linearly elastic body with [Formula: see text] as its reference configuration, and define the Hilbert space [Formula: see text] Then we recently showed that the associated pure traction problem is equivalent to finding a 2 × 2 matrix field ∊ = (∊αβ) ∈ 𝔼(Ω) that satisfies [Formula: see text] where [Formula: see text] where (Aαβστ) is the elasticity tensor, and ℓ is a continuous linear form over 𝔼(Ω) that takes into account the applied forces. Since the unknown stresses (σαβ) inside the elastic body are then given by σαβ = Aαβστ eστ, this minimization problem thus directly provides the stresses. We show here how the above Saint Venant compatibility condition ∂11 e22 - 2∂12e12 + ∂22e11 = 0 in H-2(Ω) can be exactly implemented in a finite element space 𝔼h, which uses "edge" finite elements in the sense of J. C. Nédélec. We then establish that the unique solution ϵh of the associated discrete problem, viz., find ϵh ∈ 𝔼h such that [Formula: see text] converges to ϵ in the space [Formula: see text]. We emphasize that, by contrast with a mixed method, only the approximate stresses are computed in this approach.

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12

Burazin, Krešimir, Ivana Crnjac, and Marko Vrdoljak. "Optimality criteria method in 2D linearized elasticity problems." Applied Numerical Mathematics 160 (February 2021): 192–204. http://dx.doi.org/10.1016/j.apnum.2020.10.002.

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13

Ciarlet, Philippe G., and Patrick Ciarlet. "Another approach to linearized elasticity and Korn's inequality." Comptes Rendus Mathematique 339, no. 4 (August 2004): 307–12. http://dx.doi.org/10.1016/j.crma.2004.06.021.

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14

Beylkin, G., and R. Burridge. "Linearized inverse scattering problems in acoustics and elasticity." Wave Motion 12, no. 1 (January 1990): 15–52. http://dx.doi.org/10.1016/0165-2125(90)90017-x.

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15

Gussmann, Pascal. "Linearized Elasticity as Γ-Limit of Finite Elasticity in the Case of Cracks". PAMM 13, № 1 (29 листопада 2013): 351–52. http://dx.doi.org/10.1002/pamm.201310171.

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16

Chiriţă, S., M. Ciarletta, and B. Straughan. "Structural stability in porous elasticity." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2073 (March 30, 2006): 2593–605. http://dx.doi.org/10.1098/rspa.2006.1695.

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Анотація:

We consider the linearized system of equations for an elastic body with voids as derived by Cowin & Nunziato. We demonstrate that the solution depends continuously on changes in the coefficients, which couple the equations of elastic deformation and of voids. It is also shown that the solution to the coupled system converges, in an appropriate measure, to the solutions of the uncoupled systems as the coupling coefficients tend to zero.

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17

Focardi, M., and F. Iurlano. "Asymptotic Analysis of Ambrosio--Tortorelli Energies in Linearized Elasticity." SIAM Journal on Mathematical Analysis 46, no. 4 (January 2014): 2936–55. http://dx.doi.org/10.1137/130947180.

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18

Sini, Mourad. "Absence of Positive Eigenvalues for the Linearized Elasticity System." Integral Equations and Operator Theory 49, no. 2 (June 1, 2004): 255–77. http://dx.doi.org/10.1007/s00020-002-1265-x.

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19

JOG, C. S., and HARISH P. CHERUKURI. "A reexamination of some puzzling results in linearized elasticity." Sadhana 39, no. 1 (February 2014): 139–47. http://dx.doi.org/10.1007/s12046-013-0194-5.

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20

CIARLET, PHILIPPE G., and PATRICK CIARLET. "ANOTHER APPROACH TO LINEARIZED ELASTICITY AND A NEW PROOF OF KORN'S INEQUALITY." Mathematical Models and Methods in Applied Sciences 15, no. 02 (February 2005): 259–71. http://dx.doi.org/10.1142/s0218202505000352.

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Анотація:

We describe and analyze an approach to the pure traction problem of three-dimensional linearized elasticity, whose novelty consists in considering the linearized strain tensor as the "primary" unknown, instead of the displacement itself as is customary. This approach leads to a well-posed minimization problem, constrained by a weak form of the St Venant compatibility conditions. Interestingly, it also provides a new proof of Korn's inequality.

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21

Casado-Díaz, J., and M. Luna-Laynez. "Homogenization of the anisotropic heterogeneous linearized elasticity system in thin reticulated structures." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 134, no. 6 (December 2004): 1041–83. http://dx.doi.org/10.1017/s0308210500003620.

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Анотація:

The aim of this paper is to study the asymptotic behaviour of the solutions of the linearized elasticity system, posed on thin reticulated structures involving several small parameters. We show that this behaviour depends on the relative size of the parameters. In each case, we obtain a limit system where the microstructure and macrostructure appear simultaneously. From it, we get a suitable approximation in L2 of the displacements and the linearized strain tensor.

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22

Scardia, Lucia. "Asymptotic models for curved rods derived from nonlinear elasticity by Γ-convergence". Proceedings of the Royal Society of Edinburgh: Section A Mathematics 139, № 5 (21 вересня 2009): 1037–70. http://dx.doi.org/10.1017/s0308210507000194.

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Анотація:

We study the problem of the rigorous derivation of one-dimensional models for a thin curved beam starting from three-dimensional nonlinear elasticity. We describe the limiting models obtained for different scalings of the energy. In particular, we prove that the limit functional corresponding to higher scalings coincides with the one derived by dimension reduction starting from linearized elasticity.

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23

Eberle, Sarah, and Bastian Harrach. "Shape reconstruction in linear elasticity: standard and linearized monotonicity method." Inverse Problems 37, no. 4 (March 15, 2021): 045006. http://dx.doi.org/10.1088/1361-6420/abc8a9.

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24

Kerdid, Nabil. "On the linearized system of elasticity in the half-space." AIMS Mathematics 7, no. 8 (2022): 14991–5001. http://dx.doi.org/10.3934/math.2022821.

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Анотація:

<abstract><p>The purpose of this paper is twofold. The first goal is to provide a simple and constructive proof of Korn inequalities in half-space with weighted norms. The proof leads to explicit values of the constants. The second objective is to use these inequalities to show that the linear elasticity system in half-space admits a coercive variational formulation. This formulation corresponds to the physical case in which the solution is evanescent at infinity.</p></abstract>

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25

Chambolle, Antonin. "A Density Result in Two-Dimensional Linearized Elasticity, and Applications." Archive for Rational Mechanics and Analysis 167, no. 3 (May 1, 2003): 211–33. http://dx.doi.org/10.1007/s00205-002-0240-7.

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26

Freddi, Francesco, and Gianni Royer-Carfagni. "From Non-Linear Elasticity to Linearized Theory: Examples Defying Intuition." Journal of Elasticity 96, no. 1 (February 20, 2009): 1–26. http://dx.doi.org/10.1007/s10659-009-9191-7.

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27

Fabijanic, Eva, and Josip Tambaca. "Numerical comparison of the beam model and 2D linearized elasticity." Structural Engineering and Mechanics 33, no. 5 (November 30, 2009): 621–33. http://dx.doi.org/10.12989/sem.2009.33.5.621.

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28

Angoshtari, Arzhang, and Arash Yavari. "A geometric structure-preserving discretization scheme for incompressible linearized elasticity." Computer Methods in Applied Mechanics and Engineering 259 (June 2013): 130–53. http://dx.doi.org/10.1016/j.cma.2013.03.004.

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29

BLANCHARD, DOMINIQUE, and GEORGES GRISO. "DECOMPOSITION OF DEFORMATIONS OF THIN RODS: APPLICATION TO NONLINEAR ELASTICITY." Analysis and Applications 07, no. 01 (January 2009): 21–71. http://dx.doi.org/10.1142/s021953050900130x.

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Анотація:

This paper deals with the introduction of a decomposition of the deformations of curved thin beams, with section of order δ, which takes into account the specific geometry of such beams. A deformation v is split into an elementary deformation and a warping. The elementary deformation is the analog of a Bernoulli–Navier's displacement for linearized deformations replacing the infinitesimal rotation by a rotation in SO(3) in each cross section of the rod. Each part of the decomposition is estimated with respect to the L2norm of the distance from gradient v to SO(3). This result relies on revisiting the rigidity theorem of Friesecke–James–Müller in which we estimate the constant for a bounded open set star-shaped with respect to a ball. Then we use the decomposition of the deformations to derive a few types of asymptotic geometrical behavior: large deformations of extensional type, inextensional deformations and linearized deformations. To illustrate the use of our decomposition in nonlinear elasticity, we consider a St Venant–Kirchhoff material and upon various scalings on the applied forces we obtain the Γ-limit of the rescaled elastic energy. We first analyze the case of bending forces of order δ2which leads to a nonlinear extensible model. Smaller pure bending forces give the classical linearized model. A coupled extentional-bending model is obtained for a class of forces of order δ2in traction and of order δ3in bending.

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30

Andrieux, S., and H. D. Bui. "On some nonlinear inverse problems in elasticity." Theoretical and Applied Mechanics 38, no. 2 (2011): 125–54. http://dx.doi.org/10.2298/tam1102125a.

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Анотація:

In this paper, we make a review of some inverse problems in elasticity, in statics and dynamics, in acoustics, thermoelasticity and viscoelasticity. Crack inverse problems have been solved in closed form, by considering a nonlinear variational equation provided by the reciprocity gap functional. This equation involves the unknown geometry of the crack and the boundary data. It results from the symmetry lost between current fields and adjoint fields which is related to their support. The nonlinear equation is solved step by step by considering linear inverse problems. The normal to the crack plane, then the crack plane and finally the geometry of the crack, defined by the support of the crack displacement discontinuity, are determined explicitly. We also consider the problem of a volumetric defect viewed as the perturbation of a material constant in elastic solids which satisfies the nonlinear Calderon?s equation. The nonlinear problem reduces to two successive ones: a source inverse problem and a Volterra integral equation of the first kind. The first problem provides information on the inclusion geometry. The second one provides the magnitude of the perturbation. The geometry of the defect in the nonlinear case is obtained in closed form and compared to the linearized Calderon?s solution. Both geometries, in linearized and nonlinear cases, are found to be the same.

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31

CIARLET, PHILIPPE G., GIUSEPPE GEYMONAT, and FRANÇOISE KRASUCKI. "A NEW DUALITY APPROACH TO ELASTICITY." Mathematical Models and Methods in Applied Sciences 22, no. 01 (January 2012): 1150003. http://dx.doi.org/10.1142/s0218202512005861.

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Анотація:

The displacement-traction problem of three-dimensional linearized elasticity can be posed as three different minimization problems, depending on whether the displacement vector field, or the stress tensor field, or the strain tensor field, is the unknown. The objective of this paper is to put these three different formulations of the same problem in a new perspective, by means of Legendre–Fenchel duality theory. More specifically, we show that both the displacement and strain formulations can be viewed as Legendre–Fenchel dual problems to the stress formulation. We also show that each corresponding Lagrangian has a saddle-point, thus fully justifying this new duality approach to elasticity.

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32

Javili, Ali, Niels Saabye Ottosen, Matti Ristinmaa, and Jörn Mosler. "Aspects of interface elasticity theory." Mathematics and Mechanics of Solids 23, no. 7 (April 10, 2017): 1004–24. http://dx.doi.org/10.1177/1081286517699041.

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Анотація:

Interfaces significantly influence the overall material response especially when the area-to-volume ratio is large, for instance in nanocrystalline solids. A well-established and frequently applied framework suitable for modeling interfaces dates back to the pioneering work by Gurtin and Murdoch on surface elasticity theory and its generalization to interface elasticity theory. In this contribution, interface elasticity theory is revisited and different aspects of this theory are carefully examined. Two alternative formulations based on stress vectors and stress tensors are given to unify various existing approaches in this context. Focus is on the hyper-elastic mechanical behavior of such interfaces. Interface elasticity theory at finite deformation is critically reanalyzed and several subtle conclusions are highlighted. Finally, a consistent linearized interface elasticity theory is established. We propose an energetically consistent interface linear elasticity theory together with its appropriate stress measures.

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33

SCARDIA, LUCIA. "DAMAGE AS Γ-LIMIT OF MICROFRACTURES IN ANTI-PLANE LINEARIZED ELASTICITY". Mathematical Models and Methods in Applied Sciences 18, № 10 (жовтень 2008): 1703–40. http://dx.doi.org/10.1142/s0218202508003170.

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Анотація:

A homogenization result is given for a material having brittle inclusions arranged in a periodic structure. According to the relation between the softness parameter and the size of the microstructure, three different limit models are deduced via Γ-convergence. In particular, damage is obtained as limit of periodically distributed microfractures.

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34

Hornung, Peter. "A $\Gamma$-Convergence Result for Thin Martensitic Films in Linearized Elasticity." SIAM Journal on Mathematical Analysis 40, no. 1 (January 2008): 186–214. http://dx.doi.org/10.1137/070683167.

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35

Goethem, Nicolas Van. "The Frank tensor as a boundary condition in intrinsic linearized elasticity." Journal of Geometric Mechanics 8, no. 4 (November 2016): 391–411. http://dx.doi.org/10.3934/jgm.2016013.

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36

Nakahata, K., and M. Kitahara. "Application of transverse waves to linearized inverse scattering methods in elasticity." Engineering Analysis with Boundary Elements 28, no. 3 (March 2004): 235–45. http://dx.doi.org/10.1016/s0955-7997(03)00054-7.

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37

SIDERIS, THOMAS C., and BECCA THOMASES. "LOCAL ENERGY DECAY FOR SOLUTIONS OF MULTI-DIMENSIONAL ISOTROPIC SYMMETRIC HYPERBOLIC SYSTEMS." Journal of Hyperbolic Differential Equations 03, no. 04 (December 2006): 673–90. http://dx.doi.org/10.1142/s0219891606000975.

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Анотація:

The local decay of energy is established for solutions to certain linear, multidimensional symmetric hyperbolic systems, with constraints. The key assumptions are isotropy and nondegeneracy of the associated symbols. Examples are given, including Maxwell's equations and linearized elasticity. Such estimates prove useful in treating nonlinear perturbations.

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38

Hellwig, J., R. M. P. Karlsson, L. Wågberg, and T. Pettersson. "Measuring elasticity of wet cellulose beads with an AFM colloidal probe using a linearized DMT model." Analytical Methods 9, no. 27 (2017): 4019–22. http://dx.doi.org/10.1039/c7ay01219e.

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39

JURAK, MLADEN, and JOSIP TAMBAČA. "DERIVATION AND JUSTIFICATION OF A CURVED ROD MODEL." Mathematical Models and Methods in Applied Sciences 09, no. 07 (October 1999): 991–1014. http://dx.doi.org/10.1142/s0218202599000452.

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Анотація:

A one-dimensional model of a curved rod is derived from the three-dimensional linearized elasticity. The model is obtained by taking the limit in the equilibrium equation of the three-dimensional elastic rod when the thickness of the rod goes to zero. The appropriate convergence result is proved.

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40

Fonseca, Irene, Janusz Ginster, and Stephan Wojtowytsch. "On the Motion of Curved Dislocations in Three Dimensions: Simplified Linearized Elasticity." SIAM Journal on Mathematical Analysis 53, no. 2 (January 2021): 2373–426. http://dx.doi.org/10.1137/20m1325654.

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41

Negri, Matteo, and Rodica Toader. "Scaling in fracture mechanics by Bažant law: From finite to linearized elasticity." Mathematical Models and Methods in Applied Sciences 25, no. 07 (April 14, 2015): 1389–420. http://dx.doi.org/10.1142/s0218202515500360.

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Анотація:

We consider crack propagation in brittle nonlinear elastic materials in the context of quasi-static evolutions of energetic type. Given a sequence of self-similar domains nΩ on which the imposed boundary conditions scale according to Bažant's law, we show, in agreement with several experimental data, that the corresponding sequence of evolutions converges (for n → ∞) to the evolution of a crack in a brittle linear-elastic material.

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42

Cesana, Pierluigi. "Relaxation of Multiwell Energies in Linearized Elasticity and Applications to Nematic Elastomers." Archive for Rational Mechanics and Analysis 197, no. 3 (December 10, 2009): 903–23. http://dx.doi.org/10.1007/s00205-009-0283-0.

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43

Amrouche, Cherif, Philippe G. Ciarlet, Liliana Gratie, and Srinivasan Kesavan. "New formulations of linearized elasticity problems, based on extensions of Donati's theorem." Comptes Rendus Mathematique 342, no. 10 (May 2006): 785–89. http://dx.doi.org/10.1016/j.crma.2006.03.027.

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44

Sili, Ali. "Homogenization of the linearized system of elasticity in anisotropic heterogeneous thin cylinders." Mathematical Methods in the Applied Sciences 25, no. 4 (2002): 263–88. http://dx.doi.org/10.1002/mma.264.

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45

Goriely, Alain, Rebecca Vandiver, and Michel Destrade. "Nonlinear Euler buckling." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2099 (July 8, 2008): 3003–19. http://dx.doi.org/10.1098/rspa.2008.0184.

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Анотація:

The buckling of hyperelastic incompressible cylindrical tubes of arbitrary length and thickness under compressive axial load is considered within the framework of nonlinear elasticity. Analytical and numerical methods for bifurcation are developed using the exact solution of Wilkes for the linearized problem within the Stroh formalism. Using these methods, the range of validity of the Euler buckling formula and its first nonlinear corrections are obtained for third-order elasticity. The values of the geometric parameters (tube thickness and slenderness) where a transition between buckling and barrelling is observed are also identified.

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46

Fatehiboroujeni, Soheil, Noemi Petra, and Sachin Goyal. "Linearized Bayesian inference for Young’s modulus parameter field in an elastic model of slender structures." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2238 (June 2020): 20190476. http://dx.doi.org/10.1098/rspa.2019.0476.

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Анотація:

The deformations of several slender structures at nano-scale are conceivably sensitive to their non-homogenous elasticity. Owing to their small scale, it is not feasible to discern their elasticity parameter fields accurately using observations from physical experiments. Molecular dynamics simulations can provide an alternative or additional source of data. However, the challenges still lie in developing computationally efficient and robust methods to solve inverse problems to infer the elasticity parameter field from the deformations. In this paper, we formulate an inverse problem governed by a linear elastic model in a Bayesian inference framework. To make the problem tractable, we use a Gaussian approximation of the posterior probability distribution that results from the Bayesian solution of the inverse problem of inferring Young’s modulus parameter fields from available data. The performance of the computational framework is demonstrated using two representative loading scenarios, one involving cantilever bending and the other involving stretching of a helical rod (an intrinsically curved structure). The results show that smoothly varying parameter fields can be reconstructed satisfactorily from noisy data. We also quantify the uncertainty in the inferred parameters and discuss the effect of the quality of the data on the reconstructions.

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47

Charef, Hamid, and Ali Sili. "The effective equilibrium law for a highly heterogeneous elastic periodic medium." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 143, no. 3 (May 22, 2013): 507–61. http://dx.doi.org/10.1017/s0308210511001053.

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We study the homogenization of the linearized system of elasticity standing for the equilibrium equation of a highly periodic heterogeneous elastic medium submitted to small deformations and made of two different materials: a very rigid material located in a set Fε (ε being the size of the period of the medium) of vertical fibres surrounded by a soft elastic material localized in the set Mε. The ratio between the coefficients of the elasticity tensor of the two materials is assumed to be 1/ε4. We deal with the general case without any special assumption, such as isotropy, on the material.

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48

Briane, Marc, and Gilles A. Francfort. "Loss of ellipticity through homogenization in linear elasticity." Mathematical Models and Methods in Applied Sciences 25, no. 05 (March 8, 2015): 905–28. http://dx.doi.org/10.1142/s0218202515500220.

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Анотація:

In 1993, it was shown by Geymonat, Müller and Triantafyllidis that, in the setting of linearized elasticity, a Γ-convergence result holds for highly oscillating sequences of elastic energies whose functional coercivity constant in ℝNis zero while the corresponding coercivity constant on the torus remains positive. We illustrate the range of applicability of that result by finding sufficient conditions for such a situation to occur. We thereby justify the degenerate laminate construction given by Gutiérrez in 1999. We also demonstrate that the predicted loss of strict strong ellipticity resulting from the construction by Gutiérrez is unique within a "laminate-like" class of microstructures. It will only occur for the specific micro-geometry investigated there. Our results thus confer both a rigorous, and a canonical character to those of Gutiérrez.

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49

Yahia, Mohamed Mourad Lhannafi Ait, and Hamid Haddadou. "A general homogenization result of spectral problem for linearized elasticity in perforated domains." Applications of Mathematics 66, no. 5 (May 7, 2021): 701–24. http://dx.doi.org/10.21136/am.2021.0009-20.

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50

Simpson, Henry C., and Scott J. Spector. "Applications of Estimates near the Boundary to Regularity of Solutions in Linearized Elasticity." SIAM Journal on Mathematical Analysis 41, no. 3 (January 2009): 923–35. http://dx.doi.org/10.1137/080722990.

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