The debonding of elastic inclusions and inhomogeneities

On the nucleation of cavities in planar elasticity

“…The basic conditions required for Hammerstein's theorem on the existence of solutions to (2.5) are that (i) the kernel be symmetric, (ii) the kernel be quadratically integrable and (iii) the kernel have positive eigenvalues. These conditions are seen to hold forK (= −K r ) (Levy 1991). Furthermore, a continuous solution to (2.5) will exist, provided the function F is contiuuous and such that it satisfies the condition…”

“…characterized by (2.4) in integral equations (2.2) and (2.3). Finally, it has been shown (Levy 1991) that, for remote equibiaxial loading, the inhomogeneous terms (h r , h θ ) in (2.2) and (2.3 Let Γ (θ) be a continuous and bounded function such that Γ (θ) = Γ(θ + π). For i, j fixed, split I ij into two integrals I a ij , I b ij over the subdomains (0, π) and (π, 2π), respectively.…”

“…Stable non-symmetric cavities can be expected to form as well, provided that the physical and geometrical parameters of the problem assume certain values. A general framework for the prediction of symmetric and non-symmetric cavity formation in systems subject to complex remote load and an interface force (2.1) has been presented by Levy (1991) in the form of integral equations governing the separation at a circular interface. Certain of those results are presented below without derivation.…”

“…The terms K r , K θ , h r and h θ appearing in (2.2) and (2.3) have been presented in Levy (1991). The kernel K r is symmetric and weakly singular with the form…”

The mechanics of atherosclerotic plaque rupture by inclusion/matrix interfacial decohesion

“…The solution to (1), subject to the stated displacement dependent interface traction boundary conditions, is obtained by a procedure introduced by one of the authors (Levy) and utilized in the analysis of a number of problems involving nonlinear interfacial decohesion and cavity nucleation in unbounded planar media (e.g. Levy, 1991Levy, , 1997Xie and Levy, 2007). The solution is represented as the superposition of two solutions, one for the uniform field (uniform layer without the inclusion) and the other for the local field (layer with a stressed cavity).…”