We investigate diffraction of reduced traction shear waves applied at the faces of a stationary crack in an elastic solid with microstructure, under antiplane deformation. The material behaviour is described by the indeterminate theory of couple stress elasticity and the crack is rectilinear and semi-infinite. The full-field solution of the crack problem is obtained through integral transforms and the Wiener-Hopf technique. A remarkable wave pattern appears which consists of entrained waves extending away from the crack, reflected Rayleigh waves moving along the crack, localized waves irradiating from the cracktip with, possibly, super-Rayleigh speed and body waves scattered around the crack-tip. Interestingly, the localized wave solution may be greatly advantageous for defect detection through acoustic emission. Dynamic stress intensity factors are presented, which generalize to Elastodynamics the corresponding results already obtained in the static framework. The correction brings out the important role of wave diffraction on stress concentration.

We consider an infinite bi-material plane containing a semi-infinite crack situated on a soft imperfect interface. The crack is loaded by a general asymmetrical system of forces distributed along the crack faces. On the basis of the weight function approach and the fundamental reciprocal identity, we derive the corresponding boundary integral formulation, relating physical quantities. The boundary integral equations derived in this paper in the imperfect interface setting show a weak singularity, in contrast to the perfect interface case, where the kernel is of the Cauchy type. We further present three alternative variants of the boundary integral equations which offer computationally favourable alternatives for certain sets of parameters.

Abstract. We define a weight function and analyse a problem of anti-plane shear in a bi-material strip containing a semi-infinite crack and an imperfect interface. We then present an asymptotic algorithm which uses the weight function to evaluate the coefficients in asymptotics of solutions to problems of wave propagation in a thin bi-material strip containing a periodic array of cracks situated at the interface between two materials.

Vellender, A., Mishuris, G., Piccolroaz, A. (2013). Perturbation analysis for an imperfect interface crack problem using weight function techniques. International Journal of Solids and Structures, 50 (24), 4098-4107We analyse a problem of anti-plane shear in a bi-material plane containing a semi-infinite crack situated on a soft imperfect interface. The plane also contains a small thin inclusion (for instance an ellipse with high eccentricity) whose influence on the propagation of the main crack we investigate. An important element of our approach is the derivation of a new weight function (a special solution to a homogeneous boundary value problem) in the imperfect interface setting. The weight function is derived using Fourier transform and Wiener-Hopf techniques and allows us to obtain an expression for an important constant of (which may be used in a fracture criterion) that describes the leading order of tractions near the crack sigma((0))(0) for the unperturbed problem. We present computations that demonstrate how sigma((0))(0) varies depending on the extent of interface imperfection and contrast in material stiffness. We then perform perturbation analysis to derive an expression for the change in the leading order of tractions near the tip of the main crack induced by the presence of the small defect, whose sign can be interpreted as the inclusion's presence having an amplifying or shielding effect on the propagation of the main crack. (C) 2013 Elsevier Ltd. All rights reserved.Peer reviewe

We analyse an asymptotic low-dimensional model of anti-plane shear in a thin bi-material strip containing a periodic array of interfacial cracks. Both ideal and non-ideal interfaces are considered. We find that the previously derived asymptotic models display a degree of inaccuracy in predicting standing wave eigenfrequencies and suggest an improvement to the asymptotic model to address this discrepancy. Computations demonstrate that the correction to the standing wave eigenfrequencies greatly improve the accuracy of the low-dimensional model.