Spring Boundary Conditions for Imperfect Contact Simulation in Multilayered Composites in Three-Dimensional Case

摘要

A precursor to destruction of a sample of a composite or homogeneous material is usually the formation of microcracks the growth of which leads to a failure of the whole structure. Detection of internal inhomogeneities and identification of their parameters, particularly detecting internal and surface defects by non-destructive testing requires effective mathematical models describing the diffraction of elastic waves by such defects. Dynamic behaviour of the deterioration of the zone is described by means of microcracks distribution and introduction of special boundary conditions connecting stresses and displacements along the faces of the interface. Stiffness in the spring boundary conditions is determined through the equivalence of these two models by concentration of the defects, their typical size and elastic properties of the contacting materials. Wave scattering by a single circular interface crack is considered at first using integral transforms. In order to derive the values of the stiffness in spring boundary conditions Baik-Thompson and Bostrom-Wickham approaches are extended and applied for the case of three-dimensional circular cracks. The spring stiffness is estimated and the results are compared with the results for identical materials previously published in literature. The spring model can be applied in order to identify damaged interfaces, which can be revealed via Lamb wave group velocities (the relevant examples are provided).