Effective elastic moduli of two-phase transversely isotropic composites with aligned clustered fibers

2000 ◽  
Vol 145 (1-4) ◽  
pp. 65-93 ◽  
Author(s):  
A. Bhattacharyya ◽  
D. C. Lagoudas
Keyword(s):  
Elastic Moduli ◽  
Transversely Isotropic ◽  
Effective Elastic Moduli ◽  
Two Phase

Effective Elastic Moduli of Ribbon-Reinforced Composites

1990 ◽  
Vol 57 (1) ◽  
pp. 158-167 ◽  
Author(s):  
Y. H. Zhao ◽  
G. J. Weng
Keyword(s):  
Aspect Ratio ◽  
Elastic Moduli ◽  
Volume Fraction ◽  
Transversely Isotropic ◽  
Isotropic Case ◽  
Effective Elastic Moduli ◽  
Cross Sectional ◽  
Isotropic Composite ◽  
The Matrix ◽  
The Hill

Based on the Eshelby-Mori-Tanaka theory the nine effective elastic constants of an orthotropic composite reinforced with monotonically aligned elliptic cylinders, and the five elastic moduli of a transversely isotropic composite reinforced with two-dimensional randomly-oriented elliptic cylinders, are derived. These moduli are given in terms of the cross-sectional aspect ratio and the volume fraction of the elliptic cylinders. When the aspect ratio approaches zero, the elliptic cylinders exist as thin ribbons, and these moduli are given in very simple, explicit forms as a function of volume fraction. It turns out that, in the transversely isotropic case, the effective elastic moduli of the composite coincide with Hill’s and Hashin’s upper bounds if ribbons are harder than the matrix, and coincide with their lower bounds if ribbons are softer. These results are in direct contrast to those of circular fibers. Since the width of the Hill-Hashin bounds can be very wide when the constituents have high modular ratios, this analysis suggests that the ribbon reinforcement is far more effective than the traditional fiber reinforcement.

Rigorous link between the conductivity and elastic moduli of fibre-reinforced composite materials

1995 ◽  
Vol 353 (1702) ◽  
pp. 243-278 ◽  
Keyword(s):  
Bulk Modulus ◽  
Elastic Moduli ◽  
Effective Conductivity ◽  
Transversely Isotropic ◽  
Circular Cylinders ◽  
Upper And Lower Bounds ◽  
Two Phase ◽  
Sharp Estimates ◽  
Reinforced Composite ◽  
Random Arrays

We derive rigorous cross-property relations linking the effective transverse electrical conductivity cr* and the effective transverse elastic moduli of any transversely isotropic, two-phase ‘fibre-reinforced’ composite whose phase boundaries are cylindrical surfaces with generators parallel to one axis. Specifically, upper and lower bounds are derived on the effective transverse bulk modulus k* in terms of cr* and on the effective transverse shear modulus //* in terms of cr*. These bounds enclose certain regions in the ct*-ac* and cr*-/r* planes, portions of which are attainable by certain microgeometries and thus optimal. Our bounds connecting the effective conductivity cr* to the effective bulk modulus ft* apply as well to anisotropic composites with square symmetry. The implications and utility of the bounds are explored for some general situations, as well as for specific microgeometries, including regular and random arrays of circular cylinders, hierarchical geometries corresponding to effective-medium theories, and checkerboard models. It is shown that knowledge of the effective conductivity can yield sharp estimates of the effective elastic moduli (and vice versa), even for infinite phase contrast.

Mori-Tanaka Estimates of the Overall Elastic Moduli of Certain Composite Materials

1992 ◽  
Vol 59 (3) ◽  
pp. 539-546 ◽  
Author(s):  
Tungyang Chen ◽  
George J. Dvorak ◽  
Yakov Benveniste
Keyword(s):  
Composite Materials ◽  
Elastic Moduli ◽  
Transversely Isotropic ◽  
Effective Elastic Moduli ◽  
Explicit Formulae ◽  
Cylindrically Orthotropic ◽  
Multiphase Composite

Simple, explicit formulae are derived for estimates of the effective elastic moduli of several multiphase composite materials with the Mori-Tanaka method. Specific results are given for composites reinforced by aligned or randomly oriented, transversely isotropic fibers or platelets, and for fibrous systems reinforced by aligned, cylindrically orthotropic fibers.

Rigorous Link Between the Electrical and Mechanical Properties of Composite Materials

1995 ◽  
Vol 411 ◽  
Author(s):  
S. Torquato ◽  
L. V. Gibiansky
Keyword(s):  
Mechanical Properties ◽  
Electrical Conductivity ◽  
Dielectric Constant ◽  
Composite Materials ◽  
Elastic Moduli ◽  
Effective Elastic Moduli ◽  
Two Phase ◽  
Property Relations ◽  
Isotropic Composite ◽  
Effective Electrical Conductivity

ABSTRACTCross-property relations that link rigorously the effective electrical conductivity (or dielectric constant) and the effective elastic moduli of two-phase, isotropic composite materials are discussed. The cross-property relations can be optimal in some cases, i.e., they are realized by particular microstructures. The relations are applied to specific two-phase composites as well as to cracked media.

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