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Research Papers

Wrinkling of a Fiber-Reinforced Membrane

[+] Author and Article Information
E. Shmoylova

Department of Civil and Environmental Engineering, Tufts University, Medford, MA 02155

A. Dorfmann1

Department of Civil and Environmental Engineering, Tufts University, Medford, MA 02155luis.dorfmann@tufts.edu

1

Corresponding author.

J. Appl. Mech 76(1), 011011 (Nov 05, 2008) (6 pages) doi:10.1115/1.2967888 History: Received April 20, 2007; Revised June 22, 2008; Published November 05, 2008

In this paper we investigate the response of fiber-reinforced cylindrical membranes subject to axisymmetric deformations. The membrane is considered as an incompressible material, and the phenomenon of wrinkling is taken into account by means of the relaxed energy function. Two cases are considered: transversely isotropic membranes, characterized by one family of fibers oriented in one direction, and orthotropic membranes, characterized by two family of fibers oriented in orthogonal directions. The strain-energy function is considered as the sum of two terms: The first term is associated with the isotropic properties of the base material, and the second term is used to introduce transverse isotropy or orthotropy in the mechanical response. We determine the mechanical response of the membrane as a function of fiber orientations for given boundary conditions. The objective is to find possible fiber orientations that make the membrane as stiff as possible for the given boundary conditions. Specifically, it is shown that for transversely isotropic membranes a unique fiber orientation exists, which does not affect the mechanical response, i.e., the overall behavior is identical to a nonreinforced membrane.

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Figures

Grahic Jump Location
Figure 4

The nondimensional ratios of the force in the constricting wire H to the parameter Γ versus fiber orientation η for a membrane with two families of oriented fibers. Geometric characteristics of the cylinder: L=5cm, R=0.5cm, and r0=0cm.

Grahic Jump Location
Figure 3

The nondimensional ratios of the resultant axial force F to the parameter Γ versus fiber orientation η for a membrane with two families of oriented fibers. Geometric characteristics of the cylinder: L=5cm, R=0.5cm, and r0=0cm.

Grahic Jump Location
Figure 1

The nondimensional ratios of the resultant axial force F to the parameter Γ versus fiber orientation η for a transversely isotropic membrane. Geometric characteristics of the cylinder: L=5cm, R=0.5cm, and r0=0cm.

Grahic Jump Location
Figure 2

The nondimensional ratios of the force in the constricting wire H to the parameter Γ versus fiber orientation η for a transversely isotropic membrane. Geometric characteristics of the cylinder: L=5cm, R=0.5cm, and r0=0cm.

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