Overall behavior of two-dimensional periodic composites

Sabina, Federico J.; Bravo‐Castillero, Julián; Guinovart-Dı́az, Raúl; Rodrı́guez-Ramos, Reinaldo; Valdiviezo-Mijangos, Oscar C.

doi:10.1016/s0020-7683(01)00107-x

Cited by 27 publications

(23 citation statements)

References 9 publications

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“…In Figs. 5 and 6, lines with symbols ''+'' represent the analytical results assuming a composite with empty fiber reported by Sabina, Bravo-Castillero, Guinovart-Díaz, Rodriguez-Ramos, and Valdiviezo-Mijangos, (2002). The curves corresponding to the perfect bonding (K t = 1 % 10 10 ) and empty fiber are upper and lower bounds respectively for all the curves obtained as the imperfect parameterK t belongs to the interval (0,1).…”

Section: Analysis Of Numerical Resultsmentioning

confidence: 93%

Overall properties in fibrous elastic composite with imperfect contact condition

Sabina

Guinovart-Dı́az

Rodrı́guez-Ramos

et al. 2012

International Journal of Engineering Science

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Section: Analysis Of Numerical Resultsmentioning

confidence: 93%

Overall properties in fibrous elastic composite with imperfect contact condition

Sabina

Guinovart-Dı́az

Rodrı́guez-Ramos

et al. 2012

International Journal of Engineering Science

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“…Moreover, whenever aligned fibers are taken into account, it is possible to study the problems in two dimensions, and semi-analytical results can be obtained by means of the theory of analytic functions and complex variables method (see, e.g. [30]) for cylindrical aligned fibers with circular or elliptical base, as done for example in [36,37,49,50]. The cell problems that are arising from our new formulation (108-111), (112-115), (116-119), and (120-123) are linear elastic cell problems as well, and they are in general simpler than the classical ones, as they are equipped with continuity of the auxiliary displacements and stresses, and also when discontinuties of the elastic coefficients occur they are solely driven by fine scale variations of the potentials' components.…”

Section: Multiplicative Decomposition Of the Potentialsmentioning

confidence: 99%

Effective balance equations for elastic composites subject to inhomogeneous potentials

Penta

Ramírez-Torres

Merodio

et al. 2017

Continuum Mech. Thermodyn.

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We derive the new effective governing equations for linear elastic composites subject to a body force that admits a Helmholtz decomposition into inhomogeneous scalar and vector potentials. We assume that the microscale, representing the distance between the inclusions (or fibers) in the composite, and its size (the macroscale) are well separated. We decouple spatial variations and assume microscale periodicity of every field. Microscale variations of the potentials induce a locally unbounded body force. The problem is homogenizable, as the results, obtained via the asymptotic homogenization technique, read as a well-defined linear elastic model for composites subject to a regular effective body force. The latter comprises both macroscale variations of the potentials, and non-standard contributions which are to be computed solving a well-posed elastic cell problem which is solely driven by microscale variations of the potentials. We compare our approach with an existing model for locally unbounded forces and provide a simplified formulation of the model which serves as a starting point for its numerical implementation. Our formulation is relevant to the study of active composites, such as electrosensitive and magnetosensitive elastomers.

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“…Both phases are assumed isotropic. A ''closed-form'' solution of such a problem was given by Sabina et al (2002) (in fact, the solution is obtained by adjusting the coefficients in an expansion of doubly periodic functions: Weierstrass functions and Natanzon functions). These authors recall that all elastic constants can be computed as soon as the following problems are solved:…”

Section: Comparison With Previous Solutionsmentioning

confidence: 99%

Effective properties of elastic periodic composite media with fibers

Bonnet

2007

Journal of the Mechanics and Physics of Solids

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A series solution to obtain the effective properties of some elastic composites media having periodically located heterogeneities is described. The method uses the classical expansion along Neuman series of the solution of the periodic elasticity problem in Fourier space, based on the Green's tensor, and exact expressions of factors depending on the shape of the inclusions. Some properties of convergence of the solution are presented, more specifically concerning the elasticity tensor of the reference medium, showing that the convergence occurs even for empty fibers. The solution is extended for rigid inclusions. A comparison is made with previous exact solutions for a fiber composite made of cylindrical fibers with circular cross-sections and with previous estimates. Different examples are presented for new situations concerning the study of fiber composites: composites with elliptic cross-sections and multi-phase fibrous composites. r

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Overall behavior of two-dimensional periodic composites

Cited by 27 publications

References 9 publications

Overall properties in fibrous elastic composite with imperfect contact condition

Overall properties in fibrous elastic composite with imperfect contact condition

Effective balance equations for elastic composites subject to inhomogeneous potentials

Effective properties of elastic periodic composite media with fibers

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