Static stresses in a periodically layered anisotropic elastic composite containing a periodic array of planar cracks

Summary The problem of calculating the static elastic stresses in a periodically layered anisotropic composite containing a periodic array of planar cracks is considered. We formulate the problem in terms of a system of simultaneous finite-part singular integral equations which can be solved numerically using collocation techniques. The solution of the integral equations enables relevant quantities such as the stress intensity factors to be computed. Numerical results are obtained for specific cases of the problem.     

Collinear periodic cracks in an anisotropic medium

The problem of collinear periodic cracks in an anisotropic medium is examined in this paper. By means of Stroh formalism and the conformal mapping method, we obtain general periodic solutions for collinear cracks. The corresponding stress intensity factors, crack opening displacements and strain energy release rate are found.     

Hypersingular integral equations for a thermoelastic problem of multiple planar cracks in an anisotropic medium

The problem of calculating the thermoelastic stress around an arbitrary number of arbitrarily located planar cracks in an infinite anisotropic medium is considered. The cracks open up under the action of suitably prescribed heat flux and traction. With the aid of suitable integral solutions, we reduce the problem to solving a system of Hadamard finite-part (hypersingular) integral equations. The hypersingular integral equations are solved for specific cases of the problem.     

Three collinear cracks in an infinite elastic medium

The plane strain problem of determining the distribution of stress in the vicinity of three cracks embedded in an infinite isotropic elastic medium is considered. The cracks are collinear, the two side cracks are equal in length and located symmetrically with respect to the middle crack. The surface tractions acting on the cracks are completely arbitrary. Some special cases of the loading are discussed in detail.     

An anisotropic strip weakened by an array of cracks

The paper deals with a 2-dimensional problem of an anisotropic elastic strip having an infinite row of Griffith cracks. By using integral equation approach, the problem is treated analytically. The stress intensity factor, the critical pressure and the energy required to open the crack are studied for two cases—(a) when the edges of the strip are in contact with smooth and rigid planes and (b) when the edges of the strip are free of tractions. Numerical results for the aforementioned quantities are obtained for both the cases for a specific anisotropic material and a comparison is made with the corresponding results for a strip made of an isotropic material.     

Kinked cracks in anisotropic elastic materials

The problem of a kinked crack is analysed for the most general case of elastic anisotropy. The kinked crack is modelled by means of continuous distributions of dislocations which are assumed to be singular both at the crack tips and at the kink vertex. The resulting system of singular integral equations is solved numerically using Chebyshev polynomials and the reciprocal theorem. The stress intensity factors for modes I, II and III and the generalised stress intensity factor at the vertex are obtained directly from the dislocation densities. This revised version was published online in July 2006 with corrections to the Cover Date.     

Multiple interacting planar cracks in an anisotropic multilayered medium under an antiplane shear stress: a hypersingular integral approach

The problem of determining the stress field around an arbitrary number of arbitrarily-located planar cracks in an anisotropic elastic half-space which adheres perfectly to an infinitely-long elastic strip is considered. The strip is made up of several layers of anisotropic materials which are perfectly bonded to one another. The multilayered medium is assumed to undergo an antiplane deformation. Suitable integral expressions are used to represent the displacement and the stress, leading to a system of hypersingular integral equations to be solved. For a specific example of the problem, which involves particular transversely-isotropic materials, the hypersingular integral equations are solved numerically, in order to calculate the relevant crack tip stress intensity factors.     

Four co-planar Griffith cracks in an infinite elastic medium

The dynamic in-plane problem of determining the stress and displacement due to four co-planar Griffith cracks moving steadily at a subsonic speed in a fixed direction in an infinite, isotropic, homogeneous medium under normal stress has been treated. The static problem of determining the stress and displacement in an infinite isotropic elastic medium has also been considered. In both cases, employing the Fourier integral transform, the problems have been reduced to solving a set of five integral equations. These integral equations have been solved using the finite Hilbert transform technique to obtain the exact form of crack opening displacement and stress intensity factors which are presented in the form of graphs.     

Three co-planar moving Griffith cracks in an infinite elastic medium

The dynamic in-plane problem of determining the stress and displacement due to three co-planar Griffith cracks moving steadily at a subsonic speed in a fixed direction in an infinite, isotropic, homogeneous medium under normal stress has been treated. The static problem of determining the stress and displacement around three co-planar Griffith cracks in an infinite isotropic elastic medium has also been considered. In both the cases, employing Fourier integral transform, the problems have been reduced to solving a set of four integral equations. These integral equations have been solved using finite Hilbert transform technique and Cook's result [16] to obtain the exact form of crack opening displacement and stress intensity factors which are presented in the form of graphs.     

Wave propagation in the presence of empty cracks in an elastic medium

This paper proposes the use of a traction boundary element method (TBEM) to evaluate 3D wave propagation in unbounded elastic media containing cracks whose geometry does not change along one direction. The proposed formulation is developed in the frequency domain and handles the thin-body difficulty presented by the classical boundary element method (BEM). The empty crack may have any geometry and orientation and may even exhibit null thickness. Implementing this model yields hypersingular integrals, which are evaluated here analytically, thereby surmounting one of the drawbacks of this formulation. The TBEM formulation enables the crack to be modelled as a single line, allowing the computation of displacement jumps in the opposing sides of the crack. Furthermore, if this formulation is combined with the classical BEM formulation the displacements in the opposing sides of the crack can be computed by modelling the crack as a closed empty thin body.     

Hertz contact problems for an anisotropic physically nonlinear elastic medium

Conditions under which Hertz contact problems exhibit the property of self-similarity are determined. Qualitative conclusions concerning the character of selfsimilitude solutions from which, among other things, an equation similar to the familiar Mayer equation follows, are drawn. The problem of the collision between nonlinearly elastic bodies is also examined.Moscow Institute of Radio Engineering, Electronics, and-Automated Equipment. Translated from Problemy Prochnosti, No. 12, pp. 47–53, December, 1989.     

Griffith cracks in an elastic medium in which body forces are acting

The plane strain problem of determining the distribution of stress in an infinite isotropic elastic medium containing Griffith cracks located on a single line is examined. The crack surfaces are assumed to be free from tractions, and the stress distribution in the medium is due to the action of body forces. Fourier transform methods are employed to reduce the problem to that of solving a singular integral equation of Cauchy type. The solution is completed in the case in which the medium contains a single crack. Particular distributions of concentrated loads are considered in detail, and the results are compared with those available in the literature.     

Weight function for an elliptical planar crack embedded in a homogeneous elastic medium

The method of simultaneous dual integral equations is used for obtaining the exact analytical solution for the weight function for an elliptical crack embedded in an infinite elastic solid. We show that the solution is unique and can be reduced to the known solutions for a number of particular cases.     

Diffraction of elastic waves by two coplanar Griffith cracks in an infinite transversely-isotropic medium

Summary The problem of diffraction of normally incident longitudinal waves by two parallel and coplanar Griffith cracks embedded in an infinite transversely-isotropic medium is considered. Approximate formulas are derived for stress intensity factors when the wave lengths are large compared, to the distance between the outer edges of the two cracks By taking appropriate limits we derive various interesting and new results.     

The stress intensity factors of a star-shaped array of cracks in an infinite elastic solid

The problem of determining the stress intensity factors and crack formation energy of a radial system of line cracks in an infinite elastic solid is reduced to the solution of a singular integral equation. The equation is solved numerically for the special case in which the cracks are opened by a constant pressure.