Reduction of 3D dynamic problems of elasticity for a bimaterial body with plane cracks to boundary integral equations (Q2754750)

Two elastic half-spaces made of different material are in ideal mechanical contact and contain an arbitrary number of plane cracks. Wave field is generated by self-equilibrated time-harmonic loads at the cracks faces. General solutions of elastodynamics equations are represented as sums of functions determined by the number of cracks. These functions ensure jumps of displacements on cracks sides. Representing displacements by using Helmholtz potentials, after fulfillment of boundary conditions, a system of integral equations of Helmholtz potential type is derived. The number of equations is equal to the total number of cracks multiplied by three. A particular problem for a two-material body containing a single crack perpendicular to the interface is considered. The original problem is reduced to boundary integral equations in the crack plane.