On the Specifics of Investigation for the Dynamic Problems of Cracked Layer by the Gradient Elasticity Theory

Abstract

In the context of nonclassical theory of elasticity (gradient theory of elasticity (GTE), General theory of elasticity), the problem of antiplane oscillations of a homogeneous isotropic layer with delamination is investigated. The boundary integral equation (BIE) with respect to the strain component of the delamination boundary is formulated. The BIE in contrast to linear elasticity theory are represented by irregular integrals—Cauchy-type integral and cubic singularity integral. The obtained boundary integral equation investigated numerically on the basis of quadrature formulas for singular integrals and by applying the solution to Chebyshev polynomials. The corresponding gradient solution (the strain field) are regular. To investigate the stress state in the area of the crack tips, the General Lurie theory was used. The General theory is similar to the Ru-Aifantis theory, which involves splitting the original problem in the framework of GTE into two problems—constructing the corresponding classical solution and obtaining the gradient solution from the solution of the inhomogeneous second-order differential equation with constant coefficients. The problem is investigated numerically, crack swap functions depending on wave number and gradient parameter value are constructed, and the numerical results are compared with the elastic case.