Load transfer in fibre-reinforced composites with viscoelastic matrix: an analytical study

Abstract

In A fibre-reinforced 2D composite material with elastic fibres and viscoelastic, isotropic matrix is studied. Starting from the solution of a reference-problem with elastic matrix material the elastic matrix parameters are substituted by their viscoelastic correspondents in the Laplace domain. For simplification the time-dependent solution is approximated by using limiting value theorems that give information about the time-dependent solution for t → 0 and t → ∞. Then the method of asymptotically equivalent functions is used and illustrated with examples of a steel fibre in a PMMA matrix. The analytical solutions are compared with their numerical counterparts. In summary it can be stated that this paper is a further contribution to the vast literature about the application of the correspondence principle to the solution of special problems of the linear viscoelasticity.

Stress analysis of adhesively-bonded single stepped-lap joints based on three-parameter fractional viscoelastic foundation model

“…The terms in equation ( 44) affect the accuracy of the approximation. Several algorithms [45][46][47] can be expressed in the general form of equation ( 44), including Gaver-Stehfest, Euler, fixed Talbot, and Durbin. The inverse transform can be approximated at each time instant (t > 0) by a finite linear combination of the transform values by setting Ω = 2 M in equation ( 44), where M is the Gaver's functions, α k = ln(2) and weighted coefficients ω k = ξ k ln(2).…”

Local stress distribution in composites for pulled-out fibers with axially varying bonding

“…It might be difficult to find the inverse Laplace transform, and different theorems and methods have been found in order to find or to approximate the inverse. For example, the Gaver-Stehfest algorithm (see Gaver [19] and Stehfest [43]) is a one-dimensional algorithm which does not use complex numbers (see, e.g., [8]).…”

“…This principle has been applied in different works, for example by Hashin [25] and by Reza and Shishesaz [40], on composites. Andrianov et al [8] applied this principle in order to study planar load transfer problems for fibers that are pulled out of a viscoelastic matrix.…”

Homogenization of viscoelastic composites with fibres of diamond-shaped cross-section

“…So, we can construct an interpolation formula valid for any volume fractions of the inclusions from the interval [0, 0.5]. A solution of this problem can be obtained by applying the two-point Padé approximants approach [2,3]. We give the definition of the two-point Padé approximants following [4].…”

“…For inclusion of the maximal possible volume fraction 1/2, we use the Dykhne-Keller-Mendelson formula [10,16,17]. Limiting solutions for small and large volume fractions are matched by two-point Padé approximants [2][3][4].…”