Matus V. Wave processes in elastic composite bodies with interphase and distributed thin inhomogeneities

The thesis presents the effective models and general analytical-numerical method for investigation of the wave fields and overall wave propagation phenomena in two- and three-dimensional elastic composites containing structural elements in the form of thin interphase and internal inhomogeneities. In an infinite elastic body there are inhomogeneities between the matrix and fibers of non-canonical form or disc-shaped inclusions. In the thin plate there are through holes and small width inclusions. Using singular perturbations theory, the asymptotically accurate models of dynamic interaction of interphase thin-walled inhomogeneity with adjacent components of a three-dimensional composite were constructed by introducing the effective conditions of displacement and stress jumps on a part of the delamination surface of a matrix and a volumetric inclusion (fiber), in the neighbourhood of which the inhomogeneity exists. Within the framework of such modelling, the null field (T-matrix) method was developed for numerical solution of two-dimensional problems of elastic longitudinal and transverse vertically and horizontally polarized waves scattering by a non-canonical fiber in the presence of thin interphase inhomogeneity. The null field method was genralized on the problems of bending waves scattering by through inhomogeneities of non-canonical form in thin infinite and semi-infinite plates. Incorporating the obtained solutions into Foldy dispersion relations, the analysis is extended to the effective dynamic properties of two-dimensional elastic composites with randomly distributed fibers and thin-walled interphase inhomogeneities, as well as using the solutions of boundary integral equations, three-dimensional elastic composites with ensembles of disc-shaped inclusions of different rigidities.