Compressive Strength in the Fiber Direction

Experimental Results for Fiber Buckle Wavelength versus Fiber Diameter (After Dow and Rosen [3-28]) 

REPRESENTATIVE EXTENSION MODE VOLUME ELEMENT OR TRANSVERSE MODE a b 

The analysis to find the fiber buckling load in each mode is based on the energy method described by Timoshenko and Gere [3-31], The buckling criterion is that the change in strain energy for the fiber, AUf, and for the associated matrix material, AUf, is equated to the work done by the fiber force, AW, during deformation to a buckled state, that is, 

Any deformation of the matrix material in the x-direction is ignored. Thus, the change in strain energy is presumed to be dominated by the energy of transverse (extensional) stresses. Thus, for the matrix. 

For the fibers, the change in strain energy is related to the curvature of the bent fiber, v , considered as a column in the manner of Timoshenko and Gere [3-31], 

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