Semi-analytical method for computing effective properties in elastic composite under imperfect contact

Otero, José A.; Rodrı́guez-Ramos, Reinaldo; Bravo‐Castillero, Julián; Guinovart-Dı́az, Raúl; Sabina, Federico J.; Monsiváis, G.

doi:10.1016/j.ijsolstr.2012.11.001

Cited by 29 publications

(28 citation statements)

References 11 publications

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“…In this section, a numerical method based on the finite element is proposed to solve problem (6)- (8). Since this technique is quite standard, it is rapidly outlined here.…”

Section: The Finite Element Methodsmentioning

confidence: 99%

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Behavior of laminated shell composite with imperfect contact between the layers

Guinovart-Sanjuán

Rizzoni

Rodrı́guez-Ramos

et al. 2017

Composite Structures

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The paper focuses on the calculation of the effective elastic properties of a laminated composite shell with imperfect contact between the layers. To achieve this goal, first the two-scale asymptotic homogenization method (AHM) is applied to derive the solutions for the local problems and to obtain the effective elastic properties of a two-layer spherical shell with imperfect contact between the layers. The results are compared with the numerical solution obtained by finite elements method (FEM). The limit case of a laminate shell composite with perfect contact at the interface is recovered. Second, the elastic properties of a spherical heterogeneous structure with isotropic periodic microstructure and imperfect contact is analyzed with the spherical assemblage model (SAM). The homogenized equilibrium equation for a spherical composite is solved using AHM and the results are compared with the exact analytical solution obtained with SAM.

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“…In this section, a numerical method based on the finite element is proposed to solve problem (6)- (8). Since this technique is quite standard, it is rapidly outlined here.…”

Section: The Finite Element Methodsmentioning

confidence: 99%

“…In [6][7][8][9], the authors obtained analytical expressions for the effective elastic properties of rectangular fibrous composites with imperfect contact between the matrix and the reinforcement. On the other hand, the multilayered curvilinear shell structures have received special attention in the last years.…”

Section: Introductionmentioning

confidence: 99%

Behavior of laminated shell composite with imperfect contact between the layers

Guinovart-Sanjuán

Rizzoni

Rodrı́guez-Ramos

et al. 2017

Composite Structures

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“…The comparisons between the present model with the semi-analytic method (SAM), see details in Appendix B, reported in Rodríguez-Ramos et al (2013) and Otero et al (2013) is provided in the Tables 3 and 4. Table 3 shows a comparison of the effective static coefficients computed using the aforementioned approaches for the ''Composite 1'' (C1), while changing the aspect ratio d and volume fraction h of Al 6061.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Now, using the same technique of finite element method, the plane problem on the unit cell is solved and the effective properties are calculated following the same procedure developed in Rodríguez-Ramos et al (2013) and Otero et al (2013).…”

mentioning

confidence: 99%

Dynamic homogenization for composites with embedded multioriented ellipsoidal inclusions

Sabina

Gandarrilla-Pérez

Otero

et al. 2015

International Journal of Solids and Structures

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Keywords:Composite materials Multi-oriented ellipsoidal inclusions Effective medium Dispersion and attenuation of waves Self-consistent method a b s t r a c t An analysis of wave propagation in the low-frequency domain using the self-consistent medium method (SCM) for a composite with randomly distributed ellipsoidal inclusions embedded in a matrix is studied. The constituents of which may have transversally isotropic properties. An extension of the SCM method proposed by Sabina et al. (1993) for transversally isotropic composites with several types of inclusions (different geometrical shapes and materials) is given. In that sense, the influence of the various geometrical forms of the inclusions in both, static and dynamic regimen, is analyzed. Quasi-longitudinal and quasi-transversal waves are considered as a function of the direction of incident wave. Some comparisons with previous results using the same method but considering only one type of ellipsoidal inclusions are excellent. Comparison with finite element calculations and two scale asymptotic homogenization method shows excellent results also. Dynamic effective properties, that is, dispersion and attenuation, for composites with different aspect ratios, and inclusion volume fractions are also shown.

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“…We fix two materials: one for the fiber and other for the matrix, which have the following elastic constants: E − = 70 GPa (Young's modulus) and ν − = 0.3 (Poisson's ratio) for the matrix, E + = 450 GPa is the Young's modulus for the fiber and ν + = 0.17 is the Poisson's ratio for the fiber. These type of materials are used in to obtain the effective coefficients using a FEM. Here, we also compare our results with data obtained for from such methodology.…”

Section: Circular Inclusion and Analytic Formulasmentioning

confidence: 99%

A solution for the local plane strain problems using elliptic integrals of Cauchy type

Felipe-Sosa

Otero

Solís

2016

Math Methods in App Sciences

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We consider a parallel fiber‐reinforced periodic elastic composite that present an imperfect contact of spring type between the fiber and the matrix. We use the elliptic integral of Cauchy type for solving the plane strain local problems that arise from the asymptotic homogenization method. Several general conditions are assumed, which include that the fibers are disposed of arbitrary manner in the local cell, that all fibers present contact perfect with different constants of imperfection, and that their cross section is a smooth closed arbitrary curve. We find that there are infinity solutions for these problems, and we find relations between these solutions and effective coefficients of the composite. Finally, we obtain analytic formulae for the circular fiber case and show some numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.

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Semi-analytical method for computing effective properties in elastic composite under imperfect contact

Cited by 29 publications

References 11 publications

Behavior of laminated shell composite with imperfect contact between the layers

Behavior of laminated shell composite with imperfect contact between the layers

Dynamic homogenization for composites with embedded multioriented ellipsoidal inclusions

A solution for the local plane strain problems using elliptic integrals of Cauchy type

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