Setting up a theory of stability of fibrous and laminated composites

Guz, A. N.

doi:10.1007/s10778-009-0216-5

Cited by 13 publications

(5 citation statements)

References 48 publications

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“…In the case of plastic models, the generalized concept of increasing load [26,69] is additionally used. The results obtained in this research area are reported in the monographs [12,14,28] and analyzed in the reviews [48,83,81].…”

Section: Stability Of Compressed Compositesmentioning

confidence: 99%

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Stability of elastic bodies under uniform compression (review)

Guz

2012

Int Appl Mech

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The main results on the three-dimensional theory of stability of compressible and incompressible hyperelastic simply connected bodies under uniform compression are analyzed. The problems are classified according to the type of loading (dead or follower loads, acting on the whole or a part of the surface) and the type of boundary conditions (the same conditions on the whole surface or different conditions on different parts of the surface). Approaches based on the three-dimensional linearized theory of stability (theory of finite subcritical deformations, first and second theories of small subcritical deformations, incremental-deformation theory, theory of small average rotations) and an approximate approach (linear equations; the loading parameter is approximately included in the boundary conditions) to solving these problems are discussed. Related problems (rock pressure manifestations, folding in the Earth's crust, wave-like formations on the surface of structural members, stability of laminated composite materials) are briefly commented. Regarding isotropic compressible and incompressible hyperelastic materials, the three-dimensional theory of elastic stability, theory of finite subcritical deformations, and first and second theories of small subcritical deformations are considered. The sufficient conditions for the applicability of the static (Euler's) method, the sufficient conditions for the stability of equilibrium state, and the general solutions to anti-plane, plane, and spatial problems for homogeneous subcritical states are formulated. The exact solutions, obtained with the above-mentioned general approaches, for compressible and incompressible isotropic bodies (strip, rectangular and circular plates, circular cylinder, sphere, and body of arbitrary geometry) under dead or follower loading are presented. These solutions were obtained for isotropic hyperelastic materials with an arbitrary elastic potential under uniform (hydrostatic, biaxial, or triaxial) pressure. The reviewed results were originally reported in the author's monograph (A. N. Guz, Stability of Elastic Bodies under Uniform Compression [in Russian], Naukova Dumka, Kyiv (1979)) and articles listed in the ReferencesKeywords: stability of simply connected isotropic hyperelastic bodies, three-dimensional linearized theory, uniform loading, dead follower loads Introduction.Here we provide an introductory discussion of the problem of interest and related problems, including a brief historical sketch, classification of problems, brief description of approaches, relation to phenomena observed in related fundamental and scientific-and-technological fields, and exemplary analysis of recent publications.1.1. Brief Historical Sketch. The present paper reviews results related to hyperelastic isotropic compressible or incompressible simply connected bodies with an arbitrary elastic potential. In this case (simply connected isotropic elastic bodies), uniform hydrostatic compression (of arbitrarily shaped bodies) and uniform uniaxial, biaxial, or triaxia...

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Section: Stability Of Compressed Compositesmentioning

confidence: 99%

“…1.4.1-1.4.4, the theory of stability of composites is, apparently, the most developed and based on rigorous and consistent approaches. For more details on this theory, see [12,14,28,48,81,83].…”

Section: Stability Of Compressed Compositesmentioning

confidence: 99%

Stability of elastic bodies under uniform compression (review)

Guz

2012

Int Appl Mech

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“…A thorough inspection of related research is conducted by Guz et al. 24 The TDLST is applied mainly to the stability loss of constructions produced from materials which are independent form time. The method proposed by Hoff 25 to inspect the loss of stability of structural elements made of materials which are time-dependent is focused on the study of the growth of initial unimportant defects of the construction elements with the time flow under constant external static compressive forces.…”

Section: Introductionmentioning

confidence: 99%

The stability loss of a locally curved double-walled carbon nanotube in visco-elastic matrix

Kayıkçı

Köşker

2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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In the current study, stability loss investigation is carried out for a viscoelastic medium containing a double-walled carbon nanotube with local curvature. This research has been carried out using the three dimensional linearized stability theory (TDLTS) within the framework of the piecewise-homogeneous body model. In this case, it is supposed that the carbon nanotube (CNT) has an insignificant initial local defect, and the increase of this defect with the flow of time is examined. Moreover, it is accepted as the criterion for determining the loss of stability that local curvature of the CNT starts to grow indefinitely. The values of the critical time and critical force are obtained from this criterion. In addition, van der Waals forces between the inner surface of the outer tube of the CNT and the outer surface of the inner tube of the CNT were considered. The fractional-exponential Rabotnov operator defines the composite material’s viscoelasticity properties. It is expected that the results obtained from this paper may be a useful guide in applications related to exhibiting the mechanical behavior of the composite material under consideration. Therefore, the effects of viscoelasticity towards composite materials containing a locally curved DWCNT and the limits to be considered in the production of this material are obtained.

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“…(see e.g. Piggott and Harris (1980), Lu and Mai (1994), Wagner (2001a), Fleck (1997), Guz (2009)). Further important aspects are fiber misalignment and waviness (e.g.…”

Section: Introductionmentioning

confidence: 99%

On the Effects of Interacting Anisotropic Fibers on the Microbuckling in a Composite

Lapusta¹,

Labesse-Jied²,

Samborskaya

et al. 2010

Int J Fract

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An analysis of microbuckling in a composite with anisotropic fibers under compression is presented. The modelling accounts for the fiber interaction, the distinct difference in the properties of the fibers and the matrix, and also for the presence of the external boundary. Results are calculated for cases of perfect fiber-matrix bonding. It is demonstrated that the critical loading parameters can depend essentially both on the fiber anisotropy and the fiber interaction. These factors must be properly accounted for in order to get acceptable estimations of the critical loads.

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Setting up a theory of stability of fibrous and laminated composites

Cited by 13 publications

References 48 publications

Stability of elastic bodies under uniform compression (review)

Stability of elastic bodies under uniform compression (review)

The stability loss of a locally curved double-walled carbon nanotube in visco-elastic matrix

On the Effects of Interacting Anisotropic Fibers on the Microbuckling in a Composite

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