Problems of folding in the earth’s stratified crust

Guz, A. N.; Chekhov, V. N.

doi:10.1007/s10778-007-0013-y

Cited by 27 publications

(11 citation statements)

References 36 publications

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“…They exist in composite materials 1 , geological strata 2,3 , electronic devices 4 , biological tissues 5,6 and soft actuators 7 . In many cases, stresses arise due to differences in thermal expansion [8][9][10] , chemical reactions 11 , growth 5,12 , swelling 13 , or mechanical pre-strains 14 .…”

Section: Introductionmentioning

confidence: 99%

Creases on the interface between two soft materials

et al. 2014

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Theory and experiment are presented to show that an interface between two soft materials under compression can form creases, a type of bifurcation distinct from wrinkles.While creases bifurcate from a state of flat interface by a deformation localized in space and large in amplitude, wrinkles bifurcate from a state of flat interface by a deformation nonlocal in space and small in amplitude. The interfacial creases set in at a lower critical compression than interfacial wrinkles, but higher than surface creases. The condition for the onset of interfacial creases is scale-free, and is calculated in terms of elastic moduli, pre-strains and applied strains.

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Section: Introductionmentioning

confidence: 99%

Creases on the interface between two soft materials

et al. 2014

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“…In the case of a piecewise-homogeneous subcritical stress state, the solution of Eq. (2.1) is sought in the form we use the matrix method outlined in [3,23,24]. As a result, we arrive at a system of homogeneous algebraic equations for these constants.…”

Section: Research Technique and Solution Of Specific Problemsmentioning

confidence: 99%

“…A contemporary analysis of the results on stability of layered and fibrous composites obtained by the approaches of [8,9] can be found in [5,3,11,19], including analysis of results on near-surface instability. It should be noted that the publication [12] was one of the first studies on the strict theory of surface instability of materials with periodic structure.…”

mentioning

confidence: 99%

“…It should be noted that the publication [12] was one of the first studies on the strict theory of surface instability of materials with periodic structure. The approaches of [8,9] were also used to analyze results obtained in some other research areas such as the theory of stability of mine workings [3,11] and the theory of folding in the Earth's stratified crust [3] for homogeneous and…”

mentioning

confidence: 99%

“…The results on the three-dimensional theory of stability of layered and fibrous materials with certain interface conditions were analyzed in [3,5,12,19]. Note that results on the three-dimensional theory of stability of composites with interface cracks have recently been obtained [13-17, 21, 22].…”

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confidence: 99%

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Stability of layered coatings under biaxial thermomechanical loading

Ткаченко

Chekhov

2009

Int Appl Mech

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The three-dimensional problem of stability of layered coatings at normal and high temperatures and small precritical strains is formulated and solved and the characteristic equations are derived. The temperature dependence of the physical and mechanical parameters of specific layered coatings is established experimentally. Three-layer coatings on a homogeneous substrate at different temperatures are considered as an example. Recommendations for establishing the optimal service conditions for layered structural members with coatings are formulated Introduction. The stability of layered tribotechnical coatings is analyzed in the papers [2,4,23], which indicate specific operation conditions and main types of loading for such coatings, propose design models, and give a three-dimensional problem formulation. Exact and approximate methods for solving problems for metal, polymer, and elastomer coatings on a structurally homogeneous substrate are outlined. The main types of loading in the contact region of friction elements are distributed compressive surface loads that are either follower or dead. They model the interaction of these elements in the presence of dry-film or fluid-film lubrication in the contact region. On the mid-surface of the layers, the coating and substrate are subjected to a uniformly distributed compressive load. It is assumed that the stationary temperature field in the contact region is higher than outside it. The increased temperature in the contact region was described in [4] by changing the physical and mechanical constants of the layers keeping the coating temperature constant. Each material has its specific melting temperature at which the material loses its load-bearing capacity and goes over into another aggregate state. Therefore, coatings consisting of several layers have different limiting temperatures at which there is no risk for such coatings to lose stability and, hence, to lose load-bearing capacity.The present paper gives a problem formulation, considers problem-solving methods, and solves specific problems of surface instability of layered metal coatings on a structurally homogeneous substrate under biaxial thermomechanical loading. A piecewise-homogeneous material model for linear elastic bodies is used and precritical strains are assumed small. Since we will use [1] the three-dimensional linearized theory of stability and piecewise-homogeneous model, it is expedient to mention other results obtained in solving related problems of solid mechanics in a similar formulation.The approaches to setting up theories and the basic results on the three-dimensional linearized theory of stability of deformable bodies and the three-dimensional linearized theory of elastic waves in bodies with initial (residual) stresses were analyzed in the scientific literature [8,9]. A contemporary analysis of the results on stability of layered and fibrous composites obtained by the approaches of [8,9] can be found in [5,3,11,19], including analysis of results on near-surface instability. It should be note...

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Brief Statement of Foundations of Three-Dimensional Linearized Theory of the Deformable Bodies Stability (TLTDBS)

Guz

2021

Eight Non-Classical Problems of Fracture Mechanics

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Problems of folding in the earth’s stratified crust

Cited by 27 publications

References 36 publications

Creases on the interface between two soft materials

Creases on the interface between two soft materials

Stability of layered coatings under biaxial thermomechanical loading

Brief Statement of Foundations of Three-Dimensional Linearized Theory of the Deformable Bodies Stability (TLTDBS)

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