Taking into account the structural inhomogeneity of a composite material in estimating adhesive strength

Analytical study of the interface in fibre-reinforced 2D composite material

“…Also the solutions for half-plane problems are obtained. In these cases, the solutions presented in this paper are compared with results obtained by Manevitch and Pavlenko [21,22]. Then the problems for which analytical solution are unknown are considered.…”

“…All solutions have been obtained in the closed analytical form. The method proposed by Kosmodamianskii [17] and, independently by Manevitch and Pavlenko [21,22] are applied. The comparison of the approximate solutions based on this approach with known analytical results obtained by Muki and Sternberg [31,32] show the acceptable accuracy of the proposed asymptotic simplifications.…”

“…Let us briefly discuss the asymptotic approach proposed by Manevitch and Pavlenko [21,22] (see also Andrianov et al [23]). The generalized plane stress problem for an isotropic matrix ( Fig.…”

“…On the other hand, as it has been shown by Kosmodamianskii [17], and independently by Manevitch et al [8] and by Everstine and Pipkin [18] (see also Spencer [19], and Christensen [20]), in the elastic case the strong anisotropy may allow to construct solutions with the help of an asymptotic approach using as a small parameter ε as the ratio of rigidities in the different directions. A special asymptotic technique using expansions with respect to ε gives a possibility to reduce the input biharmonic boundary value problem of the generalized plane stress problem to two harmonic boundary value problems (Manevitch and Pavlenko [8,21,22]). It has also been shown that even in the isotropic case the error involved in the first approximation is rather low.…”

Analytical study of the load transfer in fibre-reinforced 2D composite materials

“…On the other hand, as it has been shown by Kosmodamianskii (1966Kosmodamianskii ( , 1976, and independently by Manevitch et al (1970Manevitch et al ( , 1971) and by Pipkin (1971, 1973) (see also Spencer, 1974;and Christensen, 2005, Chapter 6.1), in the elastic case the strong anisotropy may allow to construct solutions with the help of an asymptotic approach using as a small parameter e the ratio of rigidities in the different directions. A special asymptotic technique using expansions with respect to e gives a possibility to reduce the input biharmonic boundary value problem of the generalized plane stress problem to two harmonic boundary value problems (Manevitch and Pavlenko, 1975, 1982Manevitch et al, 1979;Andrianov et al, 2004). It has also been shown that even in the isotropic case the error involved in the first approximation is rather low.…”