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W.j. Drugan - One of the best experts on this subject based on the ideXlab platform.

  • Dynamic stability analysis of an Elastic Composite material having a negative-stiffness phase
    Journal of the Mechanics and Physics of Solids, 2009
    Co-Authors: Dennis M. Kochmann, W.j. Drugan
    Abstract:

    The rigorous classical bounds of Elastic Composite materials theory provide limits on the achievable Composite stiffnesses in terms of the properties and arrangements of the Composite's constituents. These bounds result from the assumption, presumably made for stability reasons, that each constituent material must have positive-definite Elastic moduli. If this assumption is relaxed, recently published Elasticity analyses and experimental measurements show these bounds can be greatly exceeded, resulting in new materials of enormous potential. The key question is whether a Composite material having a non-positive-definite constituent can be stable overall in the practically useful situation of applied traction boundary conditions. Drugan 2007. Elastic Composite materials having a negative-stiffness phase can be stable. Phys. Rev. Lett. 98 (5), article no. 055502 first proved the answer is yes, by applying the energy criterion of Elastic stability to the basic two- and three-dimensional Composites consisting of a cylinder or sphere having non-positive-definite (but strongly elliptic) moduli with a thin positive-definite coating and proving overall stability provided the coating is sufficiently stiff. Here, we perform a complete and direct dynamic stability analysis of the plane strain fundamental Elastic Composite consisting of a circular cylinder of non-positive-definite material firmly bonded to a positive-definite concentric coating, for the full range of coating thicknesses (i.e., volume fractions). We determine quantitatively the full permissible range of inclusion and coating moduli, as a function of coating thickness, for which the overall Composite is stable under dead traction boundary conditions. Among the results, we show that in the thin-coating case, the present dynamic stability analysis leads to precisely the same analytical stability requirements as those derived via the energy criterion by Drugan 2007. Elastic Composite materials having a negative-stiffness phase can be stable. Phys. Rev. Lett. 98 (5), article no. 055502, and we derive new analytical stability requirements that are valid for a wider range of coating thickness. At the other extreme, we show that in the case of very thick coatings (corresponding to the dilute case of a matrix-inclusion Composite), even an inclusion with merely strongly elliptic moduli can be stabilized by a positive-definite matrix satisfying weak requirements, for which we derive analytical expressions. Overall, our results show that surprisingly weak restrictions on the moduli and thickness of the positive-definite coating are sufficient to stabilize a non-positive-definite inclusion, even one whose moduli are merely strongly elliptic. These results legitimize expanding the search for novel materials with extreme properties to those incorporating a non-positive-definite constituent, and they provide quantitative restrictions on the constituent materials' moduli and volume fractions, for the geometry examined here, that ensure overall stability of such Composite materials.

  • Elastic Composite materials having a negative stiffness phase can be stable
    Physical Review Letters, 2007
    Co-Authors: W.j. Drugan
    Abstract:

    We prove that Composite materials containing an isotropic phase having negative bulk and Young's moduli (hence being unstable by itself) can be stable overall, under merely applied traction boundary conditions, if the stable encapsulating phase is sufficiently stiff. We derive specific quantitative requirements on the Elastic moduli of the constituent materials that ensure Composite stability for two fundamental Composite geometries. These results legitimize the concept of negative-stiffness-phase Composites, thus dramatically expanding the parameter landscape in which novel and optimal overall material properties may be sought.

  • dramatically stiffer Elastic Composite materials due to a negative stiffness phase
    Journal of The Mechanics and Physics of Solids, 2002
    Co-Authors: R S Lakes, W.j. Drugan
    Abstract:

    Composite materials of extremely high stiffness can be produced by employing one phase of negative stiffness. Negative stiffness entails a reversal of the usual codirectional relationship between force and displacement in deformed objects. Negative stiffness structures and materials are possible, but unstable by themselves. We argue here that Composites made with a small volume fraction of negative stiffness inclusions can be stable and can have overall stiffness far higher than that of either constituent. This high Composite stiffness is demonstrated via several exact solutions within linearized and also fully nonlinear Elasticity, and via the overall modulus tensor estimate of a variational principle valid in this case. We provide an initial discussion of stability, and adduce experimental results which show extreme Composite behavior in selected viscoElastic systems under sub-resonant sinusoidal load. ViscoElasticity is known to expand the space of stability in some cases. We have not yet proved that purely Elastic Composite materials of the types proposed and analyzed in this paper will be stable under static load. The concept of negative stiffness inclusions is buttressed by recent experimental studies illustrating related phenomena within the Elasticity and viscoElasticity contexts.

Su-ming Xiong - One of the best experts on this subject based on the ideXlab platform.

  • 2D Green's functions for semi-infinite transversely isotropic electro-magneto-thermo-Elastic Composite
    Journal of Magnetism and Magnetic Materials, 2009
    Co-Authors: Su-ming Xiong
    Abstract:

    Green's functions play an important role in the analyses of electro-magneto-thermo-Elastic Composite. However, most works available on this topic are in case of identical temperature. Based on the compact 2D general solution of transversely isotropic electro-magneto-thermo-Elastic Composite, which is expressed in harmonic functions, and employing the trial-and-error method, the 2D Green's function for a steady point heat source in a semi-infinite electro-magneto-thermo-Elastic plane is presented by five newly induced harmonic functions. Numerical results are given graphically by contours.

Julián Bravo-castillero - One of the best experts on this subject based on the ideXlab platform.

  • Semi-analytical method for computing effective properties in Elastic Composite under imperfect contact
    International Journal of Solids and Structures, 2013
    Co-Authors: José A. Otero, Federico J. Sabina, Raúl Guinovart-díaz, Reinaldo Rodríguez-ramos, Julián Bravo-castillero, G. Monsivais
    Abstract:

    AbstractA parallel fiber-reinforced periodic Elastic Composite is considered with transversely iso-tropic constituents. Fibers with circular cross section are distributed with the same periodicity along the two perpendicular directions to the fiber orientation, i.e., the periodic cell of the Composite is square. The Composite exhibits imperfect contact, in particular, spring type at the interface between the fiber and matrix is modeled. Effective properties of this Composite for in-plane and anti-plane local problems are calculated by means of a semi-analytic method, i.e. the differential equations that described the local problems obtained by asymptotic homogenization method are solved using the finite element method. Numerical computations are implemented and comparisons with exact solutions are presented

  • Overall properties in fibrous Elastic Composite with imperfect contact condition
    International Journal of Engineering Science, 2012
    Co-Authors: Federico J. Sabina, Raúl Guinovart-díaz, Reinaldo Rodríguez-ramos, J.c. López-realpozo, Julián Bravo-castillero
    Abstract:

    Abstract In this contribution, the complete set of effective Elastic moduli are obtained by means of the asymptotic homogenization method (AHM), for two-phase fibrous periodic Composites with imperfect contact conditions of linear spring type. This work is an extension of previous reported results, where only perfect contact for Elastic Composite with square cells were considered. The constituents of the Composites exhibit transversely isotropic properties. As validation of the present method, some numerical examples and comparisons with theoretical and experimental results verified that the present model is efficient for the analysis of Composites with presence of imperfect interface. The present method can provide benchmark results for other numerical and approximate methods.

  • Two approaches for the evaluation of the effective properties of Elastic Composite with parallelogram periodic cells
    International Journal of Engineering Science, 2012
    Co-Authors: Reinaldo Rodríguez-ramos, Raúl Guinovart-díaz, J.c. López-realpozo, Harald Berger, Mathias Würkner, Ulrich Gabbert, Julián Bravo-castillero
    Abstract:

    In this work, a two-phase parallel fiber-reinforced periodic Elastic Composite is considered wherein the constituents exhibit transverse isotropy. Effective properties of fibrous Composites by means of the asymptotic homogenization method (AHM) and numerical homogenization using finite element method (FEM) are calculated for different types of parallelogram cells. Some numerical examples and comparisons with other theoretical results demonstrate that both methods are efficient for the analysis of Composites with presence of parallelogram cells. The effects of the configuration of the cells on the effective properties are observed. In general, both models predict the monoclinic behavior of the Composites.

  • Tight bounds for three-dimensional nonlinear incompressible Elastic Composites
    International Journal of Engineering Science, 2008
    Co-Authors: Ángela León-mecías, Leslie D. Pérez-fernández, Julián Bravo-castillero, Federico J. Sabina
    Abstract:

    Abstract Tighter variational bounds, in the whole range of inclusion volume fraction, that is to say, even near percolation, for the effective energy of nonlinear Composites, in the special case of 3D two-phase incompressible Elastic Composites with isotropic constituents are presented. Following the methodology of Talbot, Willis and Ponte Castaneda, a linear comparison material with the same microgeometry as the nonlinear Composite is employed. The asymptotic homogenization method (AHM) combined with a finite element analysis (FEM), is used to find the displacement field as well as the effective properties for the comparison material. An Elastic Composite with periodically distributed spherical inclusions in a cubic array is considered as an example. Various numerical examples are performed. Comparisons with others theories (i.e. variational bounds, self-consistent estimates, etc.) are shown. Coincidence of the AHM–FEM results with the universal bounds of Nemat-Nasser, Yu and Hori serves as a useful check to the numerical calculation.

  • Estimation of very narrow bounds to the behavior of nonlinear incompressible Elastic Composites
    Archive of Applied Mechanics, 2006
    Co-Authors: Leslie D. Pérez-fernández, Julián Bravo-castillero, Reinaldo Rodríguez-ramos, Federico J. Sabina
    Abstract:

    Variational bounds for the effective behavior of nonlinear Composites are improved by incorporating more-detailed morphological information. Such bounds, which are obtained from the generalized Hashin–Shtrikman variational principles, make use of a reference material with the same microstructure as the nonlinear Composite. The geometrical information is contained in the effective properties of the reference material, which are explicitly present in the analytical formulae of the nonlinear bounds. In this paper, the variational approach is combined with estimates for the effective properties of the reference Composite via the asymptotic homogenization method (AHM), and applied to a hexagonally periodic fiber-reinforced incompressible nonlinear Elastic Composite, significantly improving some recent results.

Federico J. Sabina - One of the best experts on this subject based on the ideXlab platform.

  • Semi-analytical method for computing effective properties in Elastic Composite under imperfect contact
    International Journal of Solids and Structures, 2013
    Co-Authors: José A. Otero, Federico J. Sabina, Raúl Guinovart-díaz, Reinaldo Rodríguez-ramos, Julián Bravo-castillero, G. Monsivais
    Abstract:

    AbstractA parallel fiber-reinforced periodic Elastic Composite is considered with transversely iso-tropic constituents. Fibers with circular cross section are distributed with the same periodicity along the two perpendicular directions to the fiber orientation, i.e., the periodic cell of the Composite is square. The Composite exhibits imperfect contact, in particular, spring type at the interface between the fiber and matrix is modeled. Effective properties of this Composite for in-plane and anti-plane local problems are calculated by means of a semi-analytic method, i.e. the differential equations that described the local problems obtained by asymptotic homogenization method are solved using the finite element method. Numerical computations are implemented and comparisons with exact solutions are presented

  • Overall properties in fibrous Elastic Composite with imperfect contact condition
    International Journal of Engineering Science, 2012
    Co-Authors: Federico J. Sabina, Raúl Guinovart-díaz, Reinaldo Rodríguez-ramos, J.c. López-realpozo, Julián Bravo-castillero
    Abstract:

    Abstract In this contribution, the complete set of effective Elastic moduli are obtained by means of the asymptotic homogenization method (AHM), for two-phase fibrous periodic Composites with imperfect contact conditions of linear spring type. This work is an extension of previous reported results, where only perfect contact for Elastic Composite with square cells were considered. The constituents of the Composites exhibit transversely isotropic properties. As validation of the present method, some numerical examples and comparisons with theoretical and experimental results verified that the present model is efficient for the analysis of Composites with presence of imperfect interface. The present method can provide benchmark results for other numerical and approximate methods.

  • Tight bounds for three-dimensional nonlinear incompressible Elastic Composites
    International Journal of Engineering Science, 2008
    Co-Authors: Ángela León-mecías, Leslie D. Pérez-fernández, Julián Bravo-castillero, Federico J. Sabina
    Abstract:

    Abstract Tighter variational bounds, in the whole range of inclusion volume fraction, that is to say, even near percolation, for the effective energy of nonlinear Composites, in the special case of 3D two-phase incompressible Elastic Composites with isotropic constituents are presented. Following the methodology of Talbot, Willis and Ponte Castaneda, a linear comparison material with the same microgeometry as the nonlinear Composite is employed. The asymptotic homogenization method (AHM) combined with a finite element analysis (FEM), is used to find the displacement field as well as the effective properties for the comparison material. An Elastic Composite with periodically distributed spherical inclusions in a cubic array is considered as an example. Various numerical examples are performed. Comparisons with others theories (i.e. variational bounds, self-consistent estimates, etc.) are shown. Coincidence of the AHM–FEM results with the universal bounds of Nemat-Nasser, Yu and Hori serves as a useful check to the numerical calculation.

  • Estimation of very narrow bounds to the behavior of nonlinear incompressible Elastic Composites
    Archive of Applied Mechanics, 2006
    Co-Authors: Leslie D. Pérez-fernández, Julián Bravo-castillero, Reinaldo Rodríguez-ramos, Federico J. Sabina
    Abstract:

    Variational bounds for the effective behavior of nonlinear Composites are improved by incorporating more-detailed morphological information. Such bounds, which are obtained from the generalized Hashin–Shtrikman variational principles, make use of a reference material with the same microstructure as the nonlinear Composite. The geometrical information is contained in the effective properties of the reference material, which are explicitly present in the analytical formulae of the nonlinear bounds. In this paper, the variational approach is combined with estimates for the effective properties of the reference Composite via the asymptotic homogenization method (AHM), and applied to a hexagonally periodic fiber-reinforced incompressible nonlinear Elastic Composite, significantly improving some recent results.

  • A recursive asymptotic homogenization scheme for multi-phase fibrous Elastic Composites
    Mechanics of Materials, 2005
    Co-Authors: Raúl Guinovart-díaz, Federico J. Sabina, Reinaldo Rodríguez-ramos, Julián Bravo-castillero, Jose A. Otero-hernández, Gérard A. Maugin
    Abstract:

    A multi-phase Elastic Composite is considered here. A periodic hexagonal array of concentric circular cylindrical fibers is dealt with, wherein the constituents exhibit transverse isotropy. The geometrical and transversely isotropic axes are parallel. Based on certain analytical formulae derived recently for biphasic materials using the asymptotic homogenization method, a recursive scheme is set up to determine the overall properties of this multi-phase material. Comparisons with experimental data, variational bounds and some other models are presented in order to show the efficiency of the employed scheme.

Julian Bravocastillero - One of the best experts on this subject based on the ideXlab platform.

  • closed form expressions for the effective coefficients of a fiber reinforced Composite with transversely isotropic constituents i Elastic and square symmetry
    Mechanics of Materials, 2001
    Co-Authors: Federico J. Sabina, Reinaldo Rodriguezramos, Raul Guinovartdiaz, Julian Bravocastillero
    Abstract:

    Abstract A two-phase parallel fiber-reinforced periodic Elastic Composite is considered wherein the constituents exhibit transverse isotropy. The fiber cross-section is circular and the periodicity is the same in two orthogonal directions. Simple closed-form formulae are obtained for the effective properties of this Composite by means of the asymptotic homogenization method. Numerical computation of these is easy. The analytical solution of the required resulting plane- and antiplane-strain local problems, which turns out to be only three, makes use of potential methods of a complex variable and properties of Weierstrass elliptic and related functions with periods (1,0) and (0,1). Dvorak's universal type of relations for this Composite are easily derived in an elementary new way without solving any local problem. This result also applies when the interface may be arbitrarily shaped, but compatible with the square symmetry. Comparison with experimental data is shown. The above results include the situation when one or both phases are isotropic.