The homogenized behavior of unidirectional fiber-reinforced composite materials in the case of debonded fibers

Berrehili, Yahya; Marigo, Jean‐Jacques

doi:10.2140/memocs.2014.2.181

Cited by 8 publications

(6 citation statements)

References 21 publications

(31 reference statements)

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“…The properties of the solution of the first gradient linear elasticity homogenization entail that weakly converges in ( 2 (Ω)) 3 and ( ) ∈ compact of ( −1 (Ω)) 2 . It follows then that the components of vector Although it is not the purpose of this paper to treat a homogenization problem in the framework of first gradient linear elasticity (it has been handled by other methods), one shall highlight that the results obtained with this method coincide with those obtained in the literature, see especially Berrehil [85] and Patricio and Mattheij. [86]…”

Section: Case Of First Gradient Linear Elasticitysupporting

confidence: 53%

Computation of effective piezoelectric properties of stratified composites and application to wave propagation analysis

et al. 2020

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A methodology for the computation of the homogenized response of stratified piezoelectric materials is proposed. The stratified composite consists of the periodic repetition of piezoelectric layers. Its effective piezoelectric properties are obtained through a homogenization approach based on the method of oscillating functions. The method can fully consider not only the elastic attributes, but also the polarizations of the materials contained within the structure's layers. As such, it proves able to obtain the homogenized electromechanical response of the stratified piezoelectric structure in the form of parametric, closed-form expressions, which depend on the material attributes of the layers building up the repetitive unit-cell. The applicability of the method is demonstrated for the quasi-electrostatic wave propagation analysis of stratified composites using the nonlocal piezoelectric (NLPE) theory. A two-layer stratified composite is employed, created as an assembly of LiNbO 3 and PVDF layers. The structure's homogenized properties are used to compute the wave propagation characteristics with and without the influence of internal length parameters of the NLPE theory. The obtained results suggest that the effective properties of the stratified composite can be handily used to compute the effect of the electric field on the longitudinal and shear modes for the propagation direction of interest. K E Y W O R D Shomogenization, internal length parameter, nonlocal piezoelectricity, stratified materials, wave propagation

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Section: Case Of First Gradient Linear Elasticitysupporting

confidence: 53%

Computation of effective piezoelectric properties of stratified composites and application to wave propagation analysis

et al. 2020

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“…A particular class of such microstructured materials are metamaterials, see, e.g., [13,14]. Among them let us mention fiber-reinforced composites and woven fabrics [15][16][17][18][19][20], fiber-reinforced composites with debonded fibers [21] and beam lattices [22][23][24][25], see also the report of two recent conferences [26,27]. Example of beam lattice is given in Fig.…”

Section: Introductionmentioning

confidence: 99%

On existence and uniqueness of weak solutions for linear pantographic beam lattices models

Eremeyev

Alzahrani

Cazzani

et al. 2019

Continuum Mech. Thermodyn.

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In this paper, we discuss well-posedness of the boundary-value problems arising in some “gradient-incomplete” strain-gradient elasticity models, which appear in the study of homogenized models for a large class of metamaterials whose microstructures can be regarded as beam lattices constrained with internal pivots. We use the attribute “gradient-incomplete” strain-gradient elasticity for a model in which the considered strain energy density depends on displacements and only on some specific partial derivatives among those constituting displacements first and second gradients. So, unlike to the models of strain-gradient elasticity considered up-to-now, the strain energy density which we consider here is in a sense degenerated, since it does not contain the full set of second derivatives of the displacement field. Such mathematical problem was motivated by a recently introduced new class of metamaterials (whose microstructure is constituted by the so-called pantographic beam lattices) and by woven fabrics. Indeed, as from the physical point of view such materials are strongly anisotropic, it is not surprising that the mathematical models to be introduced must reflect such property also by considering an expression for deformation energy involving only some among the higher partial derivatives of displacement fields. As a consequence, the differential operators considered here, in the framework of introduced models, are neither elliptic nor strong elliptic as, in general, they belong to the class so-called hypoelliptic operators. Following (Eremeyev et al. in J Elast 132:175–196, 2018. 10.1007/s10659-017-9660-3) we present well-posedness results in the case of the boundary-value problems for small (linearized) spatial deformations of pantographic sheets, i.e., 2D continua, when deforming in 3D space. In order to prove the existence and uniqueness of weak solutions, we introduce a class of subsets of anisotropic Sobolev’s space defined as the energy space E relative to specifically assigned boundary conditions. As introduced by Sergey M. Nikolskii, an anisotropic Sobolev space consists of functions having different differential properties in different coordinate directions.

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“…According to these results, the pantographic structure is identified with a surface composed of two families of continuously distributed fibers in the framework of continuum theory. Indeed, this kind of perspective is also justified by homogenization procedures applied to the discrete system of fibers [30][31][32][33][34][35][36]. Besides, since the fibers are modeled in accordance with the beam theory, which entails the description of their cross-section rotation, the pantographic sheets may be regarded as micropolar continua.…”

Section: Introductionmentioning

confidence: 99%

“…Scheme of an oscillatory orthogonal network of fibers. Solid blue lines are the graphs of Equation(32), while solid red lines refer to Equation(33).…”

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Equilibrium of Two-Dimensional Cycloidal Pantographic Metamaterials in Three-Dimensional Deformations

Scerrato

Giorgio

2019

Symmetry

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A particular pantographic sheet, modeled as a two-dimensional elastic continuum consisting of an orthogonal lattice of continuously distributed fibers with a cycloidal texture, is introduced and investigated. These fibers conceived as embedded beams on the surface are allowed to be deformed in a three-dimensional space and are endowed with resistance to stretching, shearing, bending, and twisting. A finite element analysis directly derived from a variational formulation was performed for some explanatory tests to illustrate the behavior of the newly introduced material. Specifically, we considered tests on: (1) bias extension; (2) compressive; (3) shear; and (4) torsion. The numerical results are discussed to some extent. Finally, attention is drawn to a comparison with other kinds of orthogonal lattices, namely straight, parabolic, and oscillatory, to show the differences in the behavior of the samples due to the diverse arrangements of the fibers.

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The homogenized behavior of unidirectional fiber-reinforced composite materials in the case of debonded fibers

Cited by 8 publications

References 21 publications

Computation of effective piezoelectric properties of stratified composites and application to wave propagation analysis

Computation of effective piezoelectric properties of stratified composites and application to wave propagation analysis

On existence and uniqueness of weak solutions for linear pantographic beam lattices models

Equilibrium of Two-Dimensional Cycloidal Pantographic Metamaterials in Three-Dimensional Deformations

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