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Purpose The purpose of this paper is to numerically investigate time-harmonic elastic wave propagation with the analysis of effective wave velocities and attenuation coefficients in a three-dimensional elastic composite consisting of infinite matrix and uniformly distributed soft, low-contrast and absolutely rigid disc-shaped micro-inclusions. Design/methodology/approach Within the assumptions of longitudinal mode of a propagating wave as well as dilute concentration and parallel orientation of inclusions in an infinite elastic matrix, Foldy’s dispersion relation is applied for introducing a complex and frequency-dependent wavenumber of homogenized structure. Then, the effective wave velocities and attenuation coefficients are directly defined from the real and imaginary parts of wavenumber, respectively. Included there a far-field forward scattering amplitude by a single low-contrast inclusion given in an analytical form, while for the other types of single scatterers it is determined from the numerical solution of boundary integral equations relative to the displacement jumps across the surfaces of soft inclusion and the stress jumps across the surfaces of rigid inclusion. Findings On the frequency dependencies, characteristic extremes of the effective wave velocities and attenuation coefficients are revealed and analyzed for different combinations of the filling ratios of involved types of inclusions. Anisotropic dynamic behavior of composite is demonstrated by the consideration of wave propagation in perpendicular and tangential directions relatively to the plane of inclusions. Specific frequencies are revealed for the first case of wave propagation, at which inclusion rigidities do not affect the effective wave parameters. Originality/value This paper develops a micromechanical study that provides a deeper understanding of the effect of thin-walled inclusions of diversified rigidities on elastic wave propagation in a three-dimensional composite. Described wave dispersion and attenuation regularities are important for the non-destructive testing of composite materials by ultrasonics.

Explicit forms of the first-order approximate boundary conditions are derived for a 2D problem of SH waves scattering by a thin, curvilinear, elastic, rigidly supported inclusion in a uniform background. The effects of varying elastic modulus and geometrical forms of the inclusion on the stress and strain states of the body near and far from the ends of the inhomogeneity are examined. The method of investigation is based on the matching of asymptotic expansions with the thickness-to-length ratio as the perturbation parameter. IntroductionThe study of wave propagation in inhomogeneous media consisting of thin-walled layers, confronts with the problem of appropriate approximations for boundary conditions and equilibrium equations of thin-walled inhomogeneities. The general purpose of the approximated boundary conditions, usually referred to as effective boundary conditions, [1, 2], or imperfect interface conditions, [3], is to simplify the analytical or numerical solutions of the wave scattering problem involving complex structures by, e.g., converting a three-media problem into a two-media problem. Such boundary conditions have been widely used in problems of wave propagation and diffraction in inhomogeneous layered media, [4, 5, 6], antenna and radar cross-section studies, [2,7], nondestructive testing of materials, [8-10], modeling of interphases in fiber-reinforced composites, [3,11,12], etc. In the latter case, the interphases constitute thin elastic layers between the fibers and the matrix, where the fiber is usually much stiffer that the matrix material. For this class of structures, only cylindrical or plane unit cell models have been used, see, e.g., [11,12].The goal of the present investigation is to obtain effective boundary conditions for elastodynamic interactions between a thin-walled, curvilinear, elastic, rigidly supported inclusion and the surrounding matrix that would hold for arbitrary values of mechanical parameters of the matrix and the inclusion in the 2D case of SH-waves scattering. The displacement asymptotic near the ends of the scatterer and the approximation of displacements over the scatterer thickness are also considered.

We have proposed a model of the elastodynamic interaction between a thin plate and a thin-walled elastic rectilinear inclusion of weak contrast. The inclusion in the plate is subjected to steady-state flexural vibrations and the conditions of perfect contact. The plate motion is described according to the Kirchhoff hypotheses. The procedure of study is based on the application of methods of the theory of singular perturbations. Using the obtained model, we have studied the spectral characteristics of flexural waves scattered by the inhomogeneity into the far-field zone.

Citation for the published paper: Kunets, Y. ; Matus, V. ; Mykhavskiv, V. et al. (2008) "Scattering of a SH-wave by an elastic fiber of nonclassical cross section with an interface crack". Mechanics of composite materials, vol. 44(2), pp. 165-172.http://dx.doi.org/10.1007/s11029-008-9002-4 Downloaded from: http://publications.lib.chalmers.se/publication/73880 Notice: Changes introduced as a result of publishing processes such as copy-editing and formatting may not be reflected in this document. For a definitive version of this work, please refer to the published source. Please note that access to the published version might require a subscription.Chalmers Publication Library (CPL) offers the possibility of retrieving research publications produced at Chalmers University of Technology. It covers all types of publications: articles, dissertations, licentiate theses, masters theses, conference papers, reports etc. Since 2006 it is the official tool for Chalmers official publication statistics. To ensure that Chalmers research results are disseminated as widely as possible, an Open Access Policy has been adopted. The CPL service is administrated and maintained by Chalmers Library.(article starts on next page) Scattering of SH-wave by an elastic fiber of non-classical cross-section with interface crack AbstractThe problem of interaction of a plane time-harmonic SH-wave with an elastic inclusion of quasi-square and quasi-triangular cross-sections, when an interface crack is present between the infinite elastic matrix and the fiber, is considered. The modified null field method taking into account the asymptotic behavior of the solution at the crack tips is exploited for obtaining the numerical results. The effects of fiber shape, inclusion/matrix materials combination, debonding (crack size) and direction of wave incidence on the scattering amplitude in the far zone are analyzed.