On the modeling of fiber dispersion in fiber-reinforced elastic materials

• We compare several models for distributed fiber reinforcement.
• A new model based on the generalized structure tensor is introduced.
• Anisotropic incompressible material can contract or expand laterally when stretched.
• Qualitative changes in behavior are used to compare the models.
• The generalized structure tensor model can be used when fiber dispersion is moderate.

When an isotropic material is subject to a uniaxial tension, the principal strain transverse to the direction of applied load is always negative. However, in fiber reinforced materials the transverse principal strain can change its sign as the load increases, passing through the zero-points, known as perversions. We investigate how the number of perversions in a material reinforced by two symmetrically aligned families of distributed fibers depends both on the degree of fiber dispersion and the model used for fiber dispersion. Angular integration and three variants of the generalized structure tensor approach are considered and discussed. The study of perversions clearly demonstrates the qualitative difference between these approaches in the case of high dispersion of fibers. The results suggest that this difference is primarily due to the way compressive fibers are modeled.