Notation
a, b	radius of fiber and matrix, respectively, in CCA model
[Aij]	a bridging tensor
$E_{11}^{\mathrm{f}}$, $E_{22}^{\mathrm{f}}$, ${\nu }_{12}^{\mathrm{f}}$, $G_{12}^{\mathrm{f}}$	longitudinal and transverse Young’s modulus, Poisson’s ratios, and shear moduli of a transversely isotropic fiber material
$E^{\mathrm{m}}$, $G^{\mathrm{m}}$, ${\nu }^{\mathrm{m}}$	Young’s modulus, Poisson’s ratio, and shear modulus of a matrix material
Vf, Vm	volume fraction of fiber and matrix, respectively
x1, x2, x3	rectangular coordinates for a lamina to represent longitudinal, transverse, and through-thickness directions, respectively
z, ρ, φ	cylindrical coordinates for a geometry with a fiber inclusion embedded in a matrix to represent longitudinal, radial, and tangential directions, respectively
α, β	bridging parameters
${\overrightarrow{R}}_{\phi }$	position vector for a point in matrix for a given φ
$K_{22}^t$	stress concentration factor of matrix in tensile direction
σ11, σ22, σ12	external stress components in composite in a rectangular coordinate system
${\sigma }_{11}^{\mathrm{f}}$,${\sigma }_{22}^{\mathrm{f}}$,${\sigma }_{12}^{\mathrm{f}}$,${\sigma }_{11}^{\mathrm{m}}$,${\sigma }_{22}^{\mathrm{m}}$,${\sigma }_{12}^{\mathrm{m}}$	planar homogenized stress components in fiber and matrix respectively in rectangular coordinate system obtained by Bridging Model
${\sigma }_{\rho \rho }^f$,${\sigma }_{\phi \phi }^{\mathrm{f}}$,${\sigma }_{\rho \phi }^{\mathrm{f}}$,${\sigma }_{\rho \rho }^{\mathrm{m}}$,${\sigma }_{\phi \phi }^{\mathrm{m}}$,${\sigma }_{\rho \phi }^{\mathrm{m}}$	planar stress components in a (z, ρ, φ) coordinate system obtained by Bridging Model.
${\tilde{\sigma }}_{22}^{\mathrm{m}}$, ${\tilde{\sigma }}_{\rho \rho }^{\mathrm{m}}$, ${\tilde{\sigma }}_{\phi \phi }^{\mathrm{m}}$, ${\tilde{\sigma }}_{\rho \phi }^{\mathrm{m}}$	pointwise stress components in matrix obtained by CCA model
${\overline{\sigma }}_{22}^{\mathrm{m}}$, ${\overline{\sigma }}_{22}^{\mathrm{f}}$	actual stress component of matrix and fiber in x2 direction
${\sigma }_{\mathrm{u},\mathrm{t}}^{\mathrm{f}}$, ${\sigma }_{\mathrm{u},\mathrm{t}}^{\mathrm{m}}$	tensile strength of a pure fiber and a pure matrix obtained from experiments
${\sigma }_{22}^{\mathrm{u},\mathrm{t}}$	ultimate tensile strength of a UD composite in transverse direction