Surface undulation instability of the viscoelastic half-space covered with the stack of layers in bi-axial compression

Akbarov, S. D.; Tekercioglu, Ramazan

doi:10.1016/j.ijmecsci.2006.09.024

Cited by 14 publications

(14 citation statements)

References 19 publications

(25 reference statements)

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“…Relevant results were obtained in [2,[18][19][20][21]82]. All these investigations assumed that the viscoelasticity of the constituents of the layered materials is …”

Section: Layered Compositesmentioning

confidence: 99%

“…The value of the parameter c corresponding to min | | p cr is taken as critical and denoted by c p cr cr = h l / . Thus, the investigations carried out in [2,[18][19][20][21]82] determined min | | p 1 0 cr and min | | p 1cr ¥ as well as c cr 0 and c cr ¥ as described above. In line with the well-known mechanical consideration, the critical time (denoted by ¢ t cr ) is determined on the assumption that the external compressive force satisfies the inequality min | | | | min | | p p p 1 1 1 0 cr cr ¥ £ £ .…”

Section: Layered Compositesmentioning

confidence: 99%

“…The paper [19] developed the approach from [18] to solve surface instability problems for a multilayered viscoelastic half-space. The approach was developed for biaxial compression and some fragments of this development are given in the present subsection.…”

Section: Layered Compositesmentioning

confidence: 99%

“…The approach was developed for biaxial compression and some fragments of this development are given in the present subsection. Moreover, specific investigations were conducted in [19] for two-dimensional (plane-strain state) and three-dimensional problems. Regarding the two-dimensional problem for a half-plane covered with two layers, the numerical results obtained in [19] coincide with those obtained in [53,58].…”

Section: Layered Compositesmentioning

confidence: 99%

“…Moreover, specific investigations were conducted in [19] for two-dimensional (plane-strain state) and three-dimensional problems. Regarding the two-dimensional problem for a half-plane covered with two layers, the numerical results obtained in [19] coincide with those obtained in [53,58]. Moreover, the critical forces and critical time were numerically obtained for a half-space (or half-plane) covered with a stack consisting of (i) a single layer, (ii) two-layers, and (iii) three layers.…”

Section: Layered Compositesmentioning

confidence: 99%

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Three-dimensional instability problems for viscoelastic composite materials and structural members

Akbarov

2007

Int Appl Mech

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Investigations of viscoelastic composite materials and structural members carried out using the TDLTSDB and initial-imperfection method are reviewed. The investigations address the internal and surface loss of stability of layered and fibrous composites, the loss of stability of plates, and the delamination (buckling) of plates with cracks. Each of these problems is reviewed separately. New areas of further research are proposed. The review focuses on the investigations carried out by the author and his students Keywords: buckling, crack, delamination, plate, instability, viscoelastic composite material 1. Introduction. As in [33,[41][42][43][44][45] and many other publications, by three-dimensional instability problems will be understood here instability problems investigated employing the three-dimensional linearized theory of stability of deformable bodies (TDLTSDB). The investigations regarding the construction of the TDLTSDB are detailed in the paper [46] and in the monographs [33,[41][42][43]45]. It was noted there that the tendencies to construct the theory, which allows us (i) to describe the buckling phenomenon for a well-defined three-dimensional stress-strain state and (ii) to obtain reliable data on the critical parameters for thin-walled and massive structural elements, contributed to the creation of the TDLTSDB. Historically, the TDLTSDB began to be developed in the first half of the 20th century, and the basic TDLTSDB relations were obtained in [30, 31-33, 35, 38, 45, 63, 71-73, 80, 84, 85] using either a strict and exact approach based on the linearization of the exact and strict relations of the nonlinear three-dimensional theory or an approximate approach based on a physical and, in part, linearization of certain relations. Development and detailed analyses of the results from these investigations were presented in the monographs [41,42,45].In the second half of the 20th century, the main attention of researchers was focused on the solution to separate classes of TDLTSDB problems. At the same time, general aspects of the TDLTSDB were also developed. It should be noted that the results of these studies were the subject of many monographs such as [41][42][43][44][45] and were reviewed in many papers such as [28,46,47,49,52,55,56,58].It follows from the search of the foregoing and other numerous inquiries that the TDLTSDB was mainly applied to analyze the stability of structural members made of time-independent materials. Moreover, these investigations used the bifurcation (Euler) approach. The Euler approach is known to be generally unsuitable for investigating instability problems for structural elements made of time-dependent materials and subjected to external static loading. This is why a dynamic investigation method was suggested in [40,45] to examine these problems. Note that this method represents the sought quantities with a multiplier exp(iWt) and determines the critical parameters of the problems from the requirement ImW = 0. However, if the dynamic investigation method is applied with...

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“…Relevant results were obtained in [2,[18][19][20][21]82]. All these investigations assumed that the viscoelasticity of the constituents of the layered materials is …”

Section: Layered Compositesmentioning

confidence: 99%