Stress-strain relations of a viscoelastic composite reinforced with elliptic cylinders

The stress-strain behaviors of a two-phase composite comprising a viscoelastic matrix and elastic elliptic cylinders are examined by means of a micromechanical theory. The reinforcing cylinders are taken to be aligned along direction 1 but randomly oriented in the 2-3 plane, with a common aspect ratio α (the thickness-to-width ratio). The strain-rate sensitivity of the stress-strain curves of the transversely isotropic composite is investigated as a function of the cross-sectional aspect ratio of the elliptic cylinders, and it is found that when the aspect ratio is one - corresponding to the traditional aligned fibers - the reinforcement is the poorest and that when the aspect ratio approaches zero - corresponding to long, thin ribbons - it is the most effective. Other types of cross-sectional aspect ratios all give rise to a stress-strain curve lying between these two. Except for the thin ribbon with α - 0 and axial tension for all, other types of reinforcement all exhibit a saturation stress under a constant strain rate and result in strong strain-rate sensitivity for the overall response of the system.