UOBScholar Hubhttps://scholarhub.balamand.edu.lbThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Mon, 15 Aug 2022 06:56:10 GMT2022-08-15T06:56:10Z50201- Deflection of multilayered composites containing wavy fibershttps://scholarhub.balamand.edu.lb/handle/uob/477Title: Deflection of multilayered composites containing wavy fibers
Authors: Rai, Habib; Honein, Elie; Najjar, Michel
Abstract: This research involves the development of theoretical model to investigate the effect of fiber waviness on the deflection of multilayered composites plates. This paper analyzes the effect of the in-plane fiber waviness on the deflection of clamped composite plate. The wavy fiber induces change in lamina elastic properties, which influence the laminate extensional, coupling, and bending stiffness. This analysis uses finite difference method, and Ritz technique to solve for deflection of multilayered composites. An example is illustrated to substantiate the model predictions. A clamped laminate containing fiber waviness subjected to transverse loading is analyzed and results of deflection versus fiber waviness are obtained.
Thu, 01 Jan 2009 00:00:00 GMThttps://scholarhub.balamand.edu.lb/handle/uob/4772009-01-01T00:00:00Z
- The effect of a crack on functionally graded fiber reinforced compositeshttps://scholarhub.balamand.edu.lb/handle/uob/505Title: The effect of a crack on functionally graded fiber reinforced composites
Authors: Honein, Elie; Rai, Habib; Honein, Tanios; Najjar, Michel
Tue, 01 Jan 2002 00:00:00 GMThttps://scholarhub.balamand.edu.lb/handle/uob/5052002-01-01T00:00:00Z
- Effect of fiber waviness on the elastic behavior of composite materialshttps://scholarhub.balamand.edu.lb/handle/uob/507Title: Effect of fiber waviness on the elastic behavior of composite materials
Authors: Rai, Habib; Honein, Elie; Najjar, Michel; Abou Abtoun, C
Tue, 01 Jan 2002 00:00:00 GMThttps://scholarhub.balamand.edu.lb/handle/uob/5072002-01-01T00:00:00Z
- Effect of the Fiber Waviness on the Stability of Laminated Plateshttps://scholarhub.balamand.edu.lb/handle/uob/513Title: Effect of the Fiber Waviness on the Stability of Laminated Plates
Authors: Rai, Habib; Honein, Elie; Najjar, Michel; Fayad, G
Wed, 01 Jan 2003 00:00:00 GMThttps://scholarhub.balamand.edu.lb/handle/uob/5132003-01-01T00:00:00Z
- A hybrid macro/micro-mechanical formulation of composites under thermo-mechanical loadinghttps://scholarhub.balamand.edu.lb/handle/uob/605Title: A hybrid macro/micro-mechanical formulation of composites under thermo-mechanical loading
Authors: Honein, Elie; Rai, Habib; Najjar, Michel; Abou Antoun, S.N
Mon, 01 Jan 2001 00:00:00 GMThttps://scholarhub.balamand.edu.lb/handle/uob/6052001-01-01T00:00:00Z
- Exact micromechanical analysis of composites with closely packed fibershttps://scholarhub.balamand.edu.lb/handle/uob/542Title: Exact micromechanical analysis of composites with closely packed fibers
Authors: Honein, Elie; Honein, Tanios; Rai, Habib; Najjar, Michel
Abstract: In this paper we show how a methodology based on the procedure of heterogenization can be implemented to solve the problem of an arbitrary number of fibers perfectly bonded to an infinite matrix which is subjected to arbitrary loading/singularities. At the heart of this methodology is a relation that exists between the solution of this heterogeneous problem and its corresponding homogeneous problem, i.e., the problem when the fibers are absent and the matrix material occupies the whole space while it is still being subjected to the same loading/singularities. This relation is universal in the sense of being independent of the loading considered. The methodology will be presented within the framework of anti-plane and plane elasticity. We proceed by considering the problem of a single fiber, then that of two fibers and we show how the result can be extended to solve for any number of fibers. This methodology leads to a new type of functional equations whose solutions are effected by novel techniques. Towards the end of the paper we touch upon the problem of two fibers in plane elasticity and we present the solution of two very challenging problems to show the efficacy of the method. © 2018, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.
Mon, 01 Jan 2018 00:00:00 GMThttps://scholarhub.balamand.edu.lb/handle/uob/5422018-01-01T00:00:00Z
- The effect of fiber waviness on the stability of laminated plates under various loadingshttps://scholarhub.balamand.edu.lb/handle/uob/508Title: The effect of fiber waviness on the stability of laminated plates under various loadings
Authors: Rai, Habib; Honein, Elie; Najjar, Michel
Abstract: This paper presents the development of an analytical formulation to predict the effect in-plane fiber waviness on the elastic stability of composite laminate. A theoretical elastic model was developed to predict the lamina elastic properties as function of fiber waviness [1]. A reduction of lamina stiffness is found due to minor fiber waviness. This formulation uses the lamina elastic properties that depend on fiber waviness, to predict the effect of fiber waviness on buckling behavior of composite plate. Percent reduction of critical buckling load versus fiber waviness is obtained. Examples are presented to substantiate the model predictions.
Sat, 01 Jan 2005 00:00:00 GMThttps://scholarhub.balamand.edu.lb/handle/uob/5082005-01-01T00:00:00Z
- The influence of fiber waviness on the reduction of critical buckling load of composites containing fiber wavinesshttps://scholarhub.balamand.edu.lb/handle/uob/634Title: The influence of fiber waviness on the reduction of critical buckling load of composites containing fiber waviness
Authors: Rai, Habib; Honein, Elie; Najjar, Michel
Abstract: The present research involves the development of theoretical model to investigate the effect of the in-plane fiber waviness on the critical shear buckling load of multilayered composite plates. This paper analyzes the in-plane shear buckling behavior of a clamped composite laminate in which fibers are considered as in-plane sinusoidal curves. The sinusoidal fiber orientation induces a change in the lamina elastic properties, which influence the laminate extensional, coupling, bending stiffness, and buckling strength. Stability of the plate is investigated and reduction of critical buckling load versus fiber waviness is obtained. The stress distribution in the layer containing fiber waviness is calculated. It was found that reduction of stiffness, and buckling loads are substantial.
Mon, 01 Jan 2007 00:00:00 GMThttps://scholarhub.balamand.edu.lb/handle/uob/6342007-01-01T00:00:00Z
- The interaction of two circular multi-layered coated fibers in a composite under arbitrary loading/singularities in anti-plane elasticityhttps://scholarhub.balamand.edu.lb/handle/uob/644Title: The interaction of two circular multi-layered coated fibers in a composite under arbitrary loading/singularities in anti-plane elasticity
Authors: Honein, Elie; Honein, Tanios; Rai, Habib; Najjar, Michel
Abstract: In this paper we present a solution, within the framework of the linear theory of elasticity, to the problem of an infinite matrix in which two parallel infinitely long circularly cylindrical inclusions are embedded. The inclusions have different radii and are formed of materials of different shear moduli. The interfaces between the matrix and the inclusions are formed of two different multi-layered interphases, The layers are coaxial cylinders of annular cross-sections with arbitrary radii and different shear moduli. The number of layers may also be arbitrary. Continuity of traction and displacement across all interfaces is assumed. The matrix is subjected to loading/singularities, which induce anti-plane deformation, but are otherwise arbitrary. The exact, analytical solution to this heterogeneous problem, when only one multi-layered fiber is present, was derived some years ago by the authors. This general solution, which is valid under arbitrary loading, to a single multi-layered coated fiber is used in this paper as a building block for a methodology of successive approximation which yields through a recursive scheme the solution of two multi-layered coated fibers. The convergence is rapid and is assured even in the extreme case when the fibers are replaced with holes touching each other. Furthermore, the accuracy can be set a priori and the series will be automatically truncated once the desired accuracy is achieved. Examples are provided, including the interaction of a screw dislocation located in the matrix with two multi-layered coated fibers. This last example can serve as a tool to model a crack as a pile-up of screw dislocations in such composite material.
Tue, 01 Jan 2013 00:00:00 GMThttps://scholarhub.balamand.edu.lb/handle/uob/6442013-01-01T00:00:00Z
- The interaction of two circular multi-layered in anti-plane elasticityhttps://scholarhub.balamand.edu.lb/handle/uob/645Title: The interaction of two circular multi-layered in anti-plane elasticity
Authors: Honein, Elie; Honein, Tanios; Rai, Habib; Najjar, Michel
Fri, 01 Jan 2016 00:00:00 GMThttps://scholarhub.balamand.edu.lb/handle/uob/6452016-01-01T00:00:00Z
- Uniform stability in nonlinear in{1C}nite delay volterra integro-di{esc}erential equations using lyapunov functionalshttps://scholarhub.balamand.edu.lb/handle/uob/2690Title: Uniform stability in nonlinear in{1C}nite delay volterra integro-di{esc}erential equations using lyapunov functionals
Authors: Raffoul, Youssef; Rai, Habib
Abstract: In [10] the fi{1C}rst author used Lyapunov functionals and studied the exponential stability of the zero solution of {1C}finite delay Volterra Integro-di{esc}erential equation. In this paper, we use modifi{1C}ed version of the Lyapunov functional that were used in [10] to obtain criterion for the stability of the zero solution of the infi{1C}nite delay nonlinear Volterra integro-differential equation .
Fri, 01 Jan 2016 00:00:00 GMThttps://scholarhub.balamand.edu.lb/handle/uob/26902016-01-01T00:00:00Z
- Micromechanical formulation of multilayered composites in thermoelasticityhttps://scholarhub.balamand.edu.lb/handle/uob/679Title: Micromechanical formulation of multilayered composites in thermoelasticity
Authors: Rai, Habib; Honein, Elie; Honein, Tanios; Najjar, Michel
Abstract: This paper presents the development of an analytical formulation to compute the stress and thermal fields in composite laminates as a result of through-the-thickness temperature gradient. The analysis couples a macro-mechanical formulation with a micro-mechanical one. The macro-mechanical formulation is based on thick laminated plate theory that enables us, among other things, to calculate the stresses and thermal gradient on the boundaries of each individual lamina. The obtained values on the boundaries of a lamina will constitute boundary conditions for a micro-mechanical problem, which is solved using the methodology of 'Heterogenization' that enables us - under the assumption that the fiber is far enough from the inter-laminar interfaces, so that the fiber can be treated as being in a matrix of infinite extent - to calculate analytically the stress and thermal fields in the lamina. The final state of stress is obtained within the matrix, inside the fiber, and at the fiber/matrix interface. The coupling of these two formulations is necessary to capture the local state of stress, which can be used to predict failure in composite lamina. An example is presented to illustrate the method. © 2001 by the American Institute of Aeronautics and Astonautics, Inc. All right reserved.
Mon, 01 Jan 2001 00:00:00 GMThttps://scholarhub.balamand.edu.lb/handle/uob/6792001-01-01T00:00:00Z
- The effect of a crack in a coated fiber reinforced compositehttps://scholarhub.balamand.edu.lb/handle/uob/1046Title: The effect of a crack in a coated fiber reinforced composite
Authors: Honein, Elie; Rai, Habib; Honein, Tanios; Chaouk, Hamdi
Sat, 01 Jan 2000 00:00:00 GMThttps://scholarhub.balamand.edu.lb/handle/uob/10462000-01-01T00:00:00Z
- Mechanics of Laminated Composites Containing Wavy Fibershttps://scholarhub.balamand.edu.lb/handle/uob/671Title: Mechanics of Laminated Composites Containing Wavy Fibers
Authors: Rai, Habib; Honein, Elie; Najjar, Michel
Abstract: Fiber waviness is fabrication induced defects in composite materials. Others have used the terms "fiber imperfections" to refer to these manufacturing defects. This defect is shown in Figure 1. It is quantified geometrically by A/L, the ratio of amplitude A to wavelength L. Fiber waviness defects have been observed to occur in, or through the thickness of, the plane of lamination. The present research involves the development of mathematical model and numerical solution methods to investigate the effect of fiber waviness on the elastic behavior and stability of composite laminate. A theoretical model is developed for a unidirectional lamina whose fiber is sinusoidal in the plane of the lamina. This model predicts the elastic properties of the lamina, bending stiffness of laminate, and critical buckling load as function of A/L.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarhub.balamand.edu.lb/handle/uob/6712006-01-01T00:00:00Z
- A novel theory of damage materials with microstuctureshttps://scholarhub.balamand.edu.lb/handle/uob/713Title: A novel theory of damage materials with microstuctures
Authors: Honein, Elie; Honein, Tanios; Rai, Habib; Najjar, Michel
Abstract: This paper presents the foundations of a novel thermodynamic theory of damage in elastic solids. The theory is rooted in the so-called "Conservative or Conventional Thermodynamics of Irreversible Processes," where the concept of a local thermodynamic state plays a prominent role. An elastic body prone to damage is regarded as a thermodynamic system characterized by a set of extensive variables that can be defined in both equilibrium and nonequilibrium states and assigned approximately the same values in both the physical space and the abstract state space (i.e., the Gibbsian phase space of constrained equilibria.) The extensive variables introduced include internal parameters which describe the damaged state of the body and whose conjugate intensive variables, or affinities, constitute a generalization of Eshelby's concept of "force on an elastic singularity." The local state approximation is applied by assigning to the entropy and temperature in physical space local values which can be calculated in the Gibbsian phase space by the well-established methods of equilibrium thermodynamics. This leads to an explicit expression for the entropy production. The rate equations for the damage are then postulated in such a way as to conform to the second part of the second law of thermodynamics. The resulting theory captures many features of real material behavior such as loading/unloading paths, quasi-ductility, dependence on the straining or loading rates, transition from brittleness to ductility with temperature rise and dependence on some global geometric parameters (size and shape) of the structure. As a further illustration of the theory, we consider the case of microcracks propagating in an elastic body (one-dimensional bar) and we include the effect of microstructure and the associated toughening mechanisms by considering a power law for the toughness curve. The stress-strain curves obtained are compared with data from experiments performed by other authors on alumina.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarhub.balamand.edu.lb/handle/uob/7132006-01-01T00:00:00Z
- A correspondence between compressible and incompressible plane elastostaticshttps://scholarhub.balamand.edu.lb/handle/uob/1804Title: A correspondence between compressible and incompressible plane elastostatics
Authors: Honein, Tanios; Honein, Elie; Najjar, Michel; Rai, Habib
Abstract: It is shown that a heretofore seemingly unnoticed correspondence (or analogy) exists between the traction boundary value problem for compressible media and the displacement boundary value problem for incompressible media occupying the same domain, in plane, isotropic, linear elastostatics. The Airy stress function, which satisfies equilibrium identically, has to be biharmonic in order to satisfy the compatibility condition in a compressible body. Correspondingly, a displacement potential function, which satisfies the incompressibility condition identically, has to be biharmonic in order to satisfy equilibrium. Since Stokes flow is governed by identical relations as incompressible plane elasticity, if displacement is interpreted as velocity and the shear modulus as dynamic viscosity, the correspondence extends to that between compressible elasticity and Stokes flow for boundary value problems indicated above. This analogy provides a rare example of a constrained system which is equivalent to the same system without the constraint.
Tue, 01 Jan 2019 00:00:00 GMThttps://scholarhub.balamand.edu.lb/handle/uob/18042019-01-01T00:00:00Z
- On multiple inhomogeneities in plane elasticityhttps://scholarhub.balamand.edu.lb/handle/uob/5677Title: On multiple inhomogeneities in plane elasticity
Authors: Honein, Elie; Najjar, Michel; Honein, Tony; Rai, Habib
Abstract: In this paper we present some new analytical techniques which have been recently developed to solve for problems of circular elastic inhomogeneities in anti-plane and plane elasticity. The inhomogeneities may be composed of different materials and have different radii. The matrix may be subjected to arbitrary loadings or singularities. The solution to this heterogeneous problem is sought as a transformation performed on the solution of the corresponding homogeneous problem, i.e., the problem when all the inhomogeneities are removed and the homogeneous matrix is subjected to the same loading/singularities, a procedure which has been dubbed ‘heterogenization’. In previous works, a single inhomogeneity or hole has been considered and the transformation has been shown to be purely algebraic in the antiplane case and involves differentiation of the Kolosov-Mushkelishvili complex potentials in the plane case. Universal formulas, i.e., formulas which are independent of the loading/singularities, that express the stresses at the interface of the inhomogeneity in terms of the stresses that would have existed at the same interface had the inhomogeneity been absent, have been be derived. The solution for a single inhomogeneity bonded to a matrix which is subjected to arbitrary loading/singularities can then in principle be used systematically in a Schwarz alternating method to obtain the solution for multiple inhomogeneities to any degree of accuracy. However alternative and innovative methods have been sought which lead to a much faster convergence and in some cases to exact expressions in terms of infinite series. The aim of this paper is to present some of the progress that has been made in this direction.
Tue, 01 Jan 2019 00:00:00 GMThttps://scholarhub.balamand.edu.lb/handle/uob/56772019-01-01T00:00:00Z
- Mechanics of laminated composite containing marcel defectshttps://scholarhub.balamand.edu.lb/handle/uob/2232Title: Mechanics of laminated composite containing marcel defects
Authors: Rai, Habib; Honein, Elie; Najjar, Michel
Abstract: Marcel is fabrication induced defects in composite materials. Others have used the terms "fiber waviness" or "fiber imperfections" to refer to these manufacturing defects. Marcel defect is shown in Fig.1. It is quantified geometrically by A/L, the ratio of amplitude A to wavelength L. Marcel defects have been observed to occur in, or through the thickness of, the plane of lamination. The present research involves the development of mathematical model and numerical solution methods to investigate the effect of marcel defects on the elastic behavior and stability of composite laminate. A theoretical model is developed for a unidirectional lamina whose fiber is sinusoidal in the plane of the lamina. This model predicts the elastic properties of the lamina and bending stiffness of laminate as function of A/L. Percent reduction of critical buckling load versus A/L is obtained.
Mon, 01 Jan 2007 00:00:00 GMThttps://scholarhub.balamand.edu.lb/handle/uob/22322007-01-01T00:00:00Z
- The material force acting on a screw dislocation in the presence of a multi-layered circular inclusionhttps://scholarhub.balamand.edu.lb/handle/uob/2223Title: The material force acting on a screw dislocation in the presence of a multi-layered circular inclusion
Authors: Honein, Elie; Rai, Habib; Najjar, Michel
Abstract: In this paper, we study the interaction of a screw dislocation with a multi-layered interphase between a circularly cylindrical inclusion and a matrix. The layers are coaxial cylinders of annular cross-sections with arbitrary radii and different shear moduli. The number of layers may also be arbitrary. Continuity of traction and displacement across all interfaces is assumed. We extend Honein et al.s solution of circularly cylindrical layered media in anti-plane elastostatics to the case where all the singularities reside inside the inclusion core. The solution to this heterogeneous problem is given explicitly, for arbitrary singularities, as a rapidly convergent Laurent series, whose coefficients are expressed in terms of those of the complex potential of a corresponding homogeneous problem with the same singularities. We then consider the two particular cases of a screw dislocation, where, in the first instance, the dislocation resides inside the matrix, while, in the second instance, it is located in the inclusion core. In both instances, the Peach–Koehler force acting on the dislocation is calculated explicitly as a rapidly convergent series. We present several examples, where the effect of the layers on the material force is examined.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarhub.balamand.edu.lb/handle/uob/22232006-01-01T00:00:00Z
- Uniform Stability in Nonlinear Infinite Delay Volterra Integro-differential Equations Using Lyapunov Functionalshttps://scholarhub.balamand.edu.lb/handle/uob/5926Title: Uniform Stability in Nonlinear Infinite Delay Volterra Integro-differential Equations Using Lyapunov Functionals
Authors: Raffoul, Youssef; Rai, Habib
Abstract: In [10] the first author used Lyapunov functionals and studied the exponential stability of the zero solution of finite delay Volterra Integro-differential equation. In this paper, we use modified version of the Lyapunov functional that were used in [10] to obtain criterion for the stability of the zero solution of the infinite delay nonlinear Volterra integro-differential equation
Sat, 02 Jan 2016 00:00:00 GMThttps://scholarhub.balamand.edu.lb/handle/uob/59262016-01-02T00:00:00Z