Wave Scattering by an Inclusion Having Imperfect Interfaces with the Matrix (original) (raw)
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Self-consistent analysis of elastic wave propagation in two-dimensional matrix-inclusion composites
Journal of the Mechanics and Physics of Solids, 1995
We present an elastodynamic effective-medium model for the calculation of the effective properties of a two-dimensional composite material consisting of an isotropic sheet with isotropic circular inclusions. Our model is used to calculate the in-plane transversal elastodynamic properties of a three-dimensional material reinforced with infinitely long cylindrical fibres. We compare these results with those of an analogous model for the transverse properties of a three-dimensional system with aligned spheroidal inclusions of finite length. The two sets of results are qualitatively similar but differ in quantitative details.
INTERFACE RESPONSE THEORY OF COMPOSITE ELASTIC MEDIA
Journal De Physique, 1989
Reçu le 2 février 1989, accepté sous forme définitive le 21 mars 1989) Résumé. 2014 Une théorie générale permettant d'étudier n'importe quel matériau élastique et composite est proposée. Son application aux composites lamellaires est ensuite développée. Ces résultats généraux sont illustrés par des exemples de nouveaux modes de vibration localisés dans des couches fluide et solide comprises entre deux autres solides semi-infinis.
The stressed state of a laminated elastic composite with a thin linear inclusion
Journal of applied mathematics and mechanics, 1995
The plane deformation of a piecewise-uniform body is investigated using the method of homogenization of an elastic medium with a maeroperiodic structure [1, 2]. The body consists of a periodic system of joined heterogeneous strips, and there is a thin elastic inclusion of finite length in one of the straight interfaces of the materials. By representing the stresses and displacements in terms of complex potentials [3] and using the conditions for the interaction of a thin elastic inclusion with the matrix [4-6] a system of four integrodifferential equations of the problem is obtained which has a solution which is appropriate for inclusions of any stiffness: from absolutely pliable, which simulates a cut, to absolutely rigid. Unlike existing solutions for defects at the interface of materials [7, 8], the solution obtained does not oscillate in the region of the tip of the inclusion.
An irregular-shaped inclusion with imperfect interface in antiplane elasticity
Acta Mechanica, 2013
Despite extensive studies of inclusions with simple shape, little effort has been devoted to inclusions of irregular shape. In this study, we consider an inclusion of irregular shape embedded within an infinite isotropic elastic matrix subject to antiplane shear deformations. The inclusion-matrix interface is assumed to be imperfect characterized by a single, non-negative, and constant interface parameter. Using complex variable techniques, the analytic function that is defined within the irregular-shaped inclusion is expanded into a Faber series, and in conjunction with the Fourier series, a set of linear algebraic equations for a finite number of unknown coefficients is determined. With this approach and without imposing any constraints on the stress distribution, a semi-analytical solution is derived for the elastic fields within the irregular-shaped inclusion and the surrounding matrix. The method is illustrated using three examples and verified, when possible, with existing solutions. The results from the calculations reveal that the stress distribution within the inclusion is highly non-uniform and depends on the inclusion shape and the weak mechanical contact at the inclusion/matrix boundary. In fact, the results illustrate that the imperfect interface parameter significantly influences the stress distribution.
International Journal of Engineering Science, 2011
We extend Eshelby's integral representations for elastic inclusion problems to the case of gradient theory of elasticity. Gradient elastic effects associated with the existence of an interphase layer, within a simple and robust gradient model whose properties are described by the harmonic equation, are discussed. The decomposition of the corresponding solution into ''classical'' and ''gradient'' components is established. It is shown that the aforementioned Eshelby-type integral formulas for gradient elasticity can be expressed in the same form as in the standard theory of elasticity, but only for the ''classical'' part of the solution. The implementation of Eshelby's approach in determining the effective properties of composites by the three-phase method requires the derivation of a complete solution for the gradient model. An example of application of the so-obtained generalized gradient method for determining the effective properties of composites with size effects due to cohesion and surface forces is given.
Composites Engineering, 1995
This paper presents a novel approach to evaluate the elastic properties and the behavior of the interphase region formed by a chemical reaction between the matrix and the fiber materials in metal matrix and ceramic matrix composites. Contrary to the traditional approach which does not allow any relative displacement at the interface without fracture, this paper considers elastic deformation of the interphase zone between the matrix and the fiber by replacing the zone by an "equivalent elastic interface". The elastic behavior of the equivalent elastic interface describes the local elastic rigidity and deformation of the interphase zone and can be quantified by a mechanics parameter called "shear stiffness coefficient" which is proportional to the ratio of the shear modulus to the local thickness of the interphase material. This paper also outlines an ultrasonic reflectivity modeling that can be used for the experimental measurement of the interfacial shear stiffness coefficient along the length of an embedded fiber. Further, an experimental method of _^^^_._^___. _C&l__ _l_____r:rc____ ___=LY_:__r :. __..._I. >. ..> .~~~.~:~~~ ~I-*, ~~~ LIICLWUISIIIGLII ~1 one 51~='81 b~uin~sb cuelllclrnt IS presenren ann expenmenrauy measured vaiues are tabulated. The significance of the quantification of such a parameter is that the elastic property of the interface obtained can be used as a common basis among material scientists designing and developing the composite systems, and groups studying material behavior for life prediction. Also, the parameter can be used by production engineers to assure that the designed properties of the composite are being achieved, and by the end users to ensure that the designed and produced properties are being retained in use.
Effect of Defects, Inclusions and Inhomogeneities in Elastic Solids
2019
This thesis focusses on the theory of materials with defects introduced by John D. Eshelby in the 50s and the 60s, which today we call Configurational Mechanics or, in his honour, Eshelbian Mechanics. The thesis consists of four interconnected parts. The first part is dedicated to the relation between two of Eshelby's developments: the energy momentum tensor (or Eshelby stress tensor), describing the net force on a defect, and the Eshelby fourth-order tensor, which relates the strain in an inclusion in an otherwise homogeneous and isotropic matrix to the virtual strain (transformation strain) defining the geometrical misfit between inclusion and matrix, within the theory of small deformations. The second part of the research was prompted by the fact that, although the relation between Eshelby's inclusion problem (Eshelby, 1951, 1975) and Noether's theorem has been mentioned in literature, no explicit relation has ever been given, to the best of our knowledge. In a framew...
Delaminated thin elastic inclusions inside elastic bodies
Mathematics and Mechanics of Complex Systems, 2014
We propose a model for a two-dimensional elastic body with a thin elastic inclusion modeled by a beam equation. Moreover, we assume that a delamination of the inclusion may take place resulting in a crack. Nonlinear boundary conditions are imposed at the crack faces to prevent mutual penetration between the faces. Both variational and differential problem formulations are considered, and existence of solutions is established. Furthermore, we study the dependence of the solution on the rigidity of the embedded beam. It is proved that in the limit cases corresponding to infinite and zero rigidity, we obtain a rigid beam inclusion and cracks with nonpenetration conditions, respectively. Anisotropic behavior of the beam is also analyzed.