Kalynyak O. Non-stationary deformation of three-dimensional elastic matrix with contrast disk-shaped inclusions

Thesis is dedicated to investigate non-stationary elastic wave propagation in a three-dimensional infinite matrix with single and multiple movable rigid and compliant disc-shaped inclusions by the time-domain BIEs method. Proposed approach doesn't impose restrictions on the disturbance scenarios, the shape, number and mutual location of inclusions. For the first time, considered problems are reduced to the BIEs of the wave potential type relative to the dynamic stress jumps (for rigid inclusions) and dynamic displacement jumps (for compliant ones) across the inhomogeneities by satisfying the wave loading conditions on the inclusions via constructed integral representations of the solutions. In the case of rigid inclusions the completeness of BIEs is achieved by accompanying them with the differential equations of motion of inclusions as the rigid units. Convergence of proposed marching (step by step) algorithm of analytic-numerical solution of BIEs is provided by their regularization procedures and precise definition of temporal convolution integrals with considering the limited time retardation in the kernels and local behavior of solutions in the neighborhood of thin inhomogeneities, and by appropriate choice of intervals of time and space boundary-element discretization. For a single inclusion in the non-stationary elastic waves field new results concerning the influences of time profiles and polarizations of wave loading, inclusions rigidity, mass and shape on the DSIF in the inhomogeneity vicinities, and translation and rotation of rigid inclusion as the functions of time have been obtained. For the systems of inclusions in an elastic matrix the inertial effects of their interaction depending on mutual location and mass ratio have been analyzed in details.