3-D dynamic interaction between a penny-shaped crack and a thin interlayer joining two elastic half-spaces

Abstract

elastodynamic interaction between a penny-shaped crack and a thin elastic interlayer joining two elastic half-spaces is investigated by an improved boundary integral equation method or boundary element method. The pennyshaped crack is embedded in one of the half-spaces, perpendicular to the interlayer and subjected to a time-harmonic tensile loading on its surfaces. Effective "spring-like" boundary conditions are applied to approximate the effects of the thin layer in the mathematical model. Integral representations for the displacement and the stress components are derived by using modified Green's functions, which satisfy the "spring-like" boundary conditions identically. Then, application of the dynamic loading condition on the crack-surfaces results in a boundary integral equation (BIE) for the crack-opening-displacement over the crack-surfaces only. A solution procedure is developed for solving the BIE numerically. Numerical results for the mode-I dynamic stress intensity factor V. Mykhas'kiv · I. Zhbadynskyi (SIF) are presented and discussed to show the variations of the mode-I dynamic SIF with the angular coordinate of the crack-front points, the dimensionless wave number, the material mismatch and the crack-layer distance.

Modelling Crack Closure for an Interface Crack Under Harmonic Loading

“…Due to the substantially more complex solution, if compared to the case of cracks in homogeneous materials, the possible contact interaction was neglected in the above papers. A similar simplification was also used by Bouden et al (1991), Zhang (1991), Qu (1994Qu ( , 1995, Wang and Gross (2001), Mykhas'kiv et al (2009), Wünsche et al (2009). To overcome the difficulties and to avoid the regularization and numerical evaluation of the hypersingular integrals, the modified system of boundary integral equations was proposed by Menshykova et al (2009).…”

Dynamic Stress Concentration at the Boundary of an Incision at the Plate Under the Action of Weak Shock Waves

“…=̃2 , (13) where: = ( ), 0 < < 2 is a set of parametric boundary equations, = ( , ), = ( , ), = 1, 2; = ( ), = ( ), = ℎ, = + ℎ 2 , ℎ = 2 , is a set of points of the partition boundaries, ̃1 ,̃2 are known functions, which are determined by (4). After determination of the unknown functions, dynamic stresses of the plate are calculated by dependencies, which are obtained in accordance with representation (7) by providing singular components in the kernels of equations and consequently using Plemelj-Sokhotski formulas:…”

The discontinuous solutions of Lame’s equations for a conical defect

“…The construction of their analytical solutions, analysis of wave fields in the vicinity of t defects constitute a broad class of problems whose decompositions require the involvement of complex mathematical apparatus. The development of this mathematical apparatus has been carried out by many scientists [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. One of the powerful methods for solving problems of wave diffraction on defects of various forms is the method of discontinuous solutions.…”