Determination of the Stress State of a Piecewise Homogeneous Elastic Body with a Row of Cracks on an Interface Surface Subject to Antiplane Strains with Inclusions at the Tips

Abstract

The stress state of a bimaterial elastic body that has a row of cracks on an interface surface is considered. It is subjected to antiplane deformations by uniformly distributed shear forces acting on the horizontal sides of the body. The governing equations of the problem, the stress intensity factors, the deformation of the crack edges, and the shear stresses are derived. The solution of the problem via the Fourier sine series is reduced to the determination of a singular integral equation (SIE) and consequently to a system of linear equations. In the end, the problem is solved in special cases with inclusions. The results of this paper and the previously published results show that the used approach based on the Gauss-Chebyshev quadrature method can be considered as a generalized procedure to solve the collinear crack problems in mode I, II, or III loadings.

Summability Methods for Elastic Local Fields in Periodic Heterogeneous Materials

“…The Fourier series are widely used in engineering [1,2]. In the mechanics of solids and structures, Fourier series are frequently adopted for finding numerical and analytic solutions [3][4][5]. Geometric, mechanical properties, and local fields in heterogeneous materials with periodic microstructure seem to be naturally suited to being represented with periodic functions, but Fourier series and relevant partial sums exhibit large oscillations, known as Gibbs phenomenon, at the jump discontinuity of the field they represent.…”