Нелинейная задача о межматериальной трещинепод воздействием волны сдвига

Abstract

Solution of the problem for an interface crack under the action of a harmonic shear wave is presented. It is shown that the same problems solutions of other authors were performed without taking into account the crack faces contact, and results obtained indicate the interpenetration of the faces, that is not possible. Thus, it is proved that the problem is nonlinear because the positions and sizes of the contact zone are unknown and variable during the loading. The solution is obtained by the boundary integral equations method taking into account the contact interaction of the crack faces: using the Somigliana dynamic identity and the boundary equations arising from them, the transition from the two-dimensional problem to the equivalent problem at the boundaries of the domain is realized; the vector components in the boundary integral equations are presented by Fourier series, to prevent the interpenetration of the crack faces and the emergence of tensile forces in the contact zone the Signorini unilateral constraints are involved. The numerical solution is performed by the method of boundary elements with constant approximation of the problem parameters on an element. Numerical researches of the shear wave frequency influence onto the crack faces and adjoining surface displacements, opening and extent of crack faces contact zone are carried out. The quantitative difference between the maximum tangential and normal components of adhesion line and the crack faces displacements is shown. It is shown that the position and length of the contact area change during the load period, and the magnitudes of the contact forces vary along the crack length.