A 3-D Periodic Instability Model for a Series of Fibres in a Matrix

Guz, A. N.; Lapusta, Yuri; Samborska, A.N.

doi:10.1177/096369350000900201

Cited by 2 publications

(2 citation statements)

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“…2 and were detailed in [52]. Let us examine only specific numerical results that were obtained in [52,[45][46][47]62] and illustrate the capabilities for the analysis of numerical results related to the problems formulated here (in Sec. 2 for fibrous composites and in Sec.…”

Section: Remarksmentioning

confidence: 99%

“…Buckling problems for one infinite periodic row of fibers in a matrix arise when fibers within the same row interact, but fibers of different rows do not interact during buckling, which is because of the nonuniform arrangement of fibers. Thus, the methods for solving buckling problems for one row of fibers in a matrix [52,[45][46][47]62] follow from the methods for solving buckling problems for a doubly periodic system of fibers in a matrix when a ® ¥ or b ® ¥ in Fig. 7.…”

Section: Remarksmentioning

confidence: 99%

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Setting up a theory of stability of fibrous and laminated composites

Guz

2009

Int Appl Mech

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The results obtained in setting up a theory of stability of fibrous and laminated composites in the case where the plane P is in an arbitrary position are analyzed. The plane P is formed by the points of a buckling mode that have equal phases relative to the line of compression. This theory follows from the linearized three-dimensional theory of stability of deformable bodies and is used to determine the critical compressive load and the associated position of the plane P. Numerical examples are presented. A brief historical sketch is given Keywords: theory of stability, fibrous and laminated composites, equiphase plane, linearized three-dimensional theory of stability of deformable bodies 1. Analysis of Problem Development. The publications [1,2] were the first to propose, in 1969, approaches based on the three-dimensional linearized theory of stability of deformable bodies (TLTSDB) to set up a theory of stability of fibrous and laminated composites under compression. For example, a fibrous composite was modeled in [1] by a piecewise-homogeneous material (TLTSDB was applied individually to the fiber reinforcement and to the matrix, and the stress and displacement vectors were assumed continuous at the interfaces) and continuum theory (a composite was modeled by an orthotropic homogeneous material with effective constants) was used in [2]. The papers [1, 2] addressed polymer-matrix composites and modeled the reinforcement and the matrix by elastic bodies. Later, the approaches of [1, 2] were extended to metal-matrix composites with the matrix modeled by an elastoplastic body.Thus, the stability analysis of polymer-and metal-matrix composites compressed along the reinforcement (fibers or layers) and modeled by a piecewise-homogeneous material employs the TLTSDB and the design models shown in Fig. 1 for fibrous composites and in Fig. 2 for laminated composites. In what follows, we will discuss issues associated with setting up the theory of stability of fibrous and laminated polymer-or metal-matrix composites. The theory models composites by a piecewise-homogeneous material, applies the TLTSDB individually to the reinforcement and to the matrix, assumes continuity of the stress and displacement vectors at the interfaces, and considers various types of structure of composites.With such an approach, internal instability (microbuckling) determined not by the configuration of a structural element and the boundary conditions on its surface, but by the stiffnesses and concentrations of the reinforcement and the matrix. In this connection, composites are assumed infinite. In studying near-surface buckling, it is naturally assumed that composites occupy a half-space and buckling modes decay with distance from its boundary.It should be noted that the most general and accurate approach to the analysis of the internal and surface instability of composites is based on the piecewise-homogeneous model [1] and the TLTSDB (the TLTSDB equations are presented in [3][4][5]18], and this theory is best detailed in [5, 18], which will b...

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