The behavior of some simple directionally reinforced incompressible nonlinearly elastic solids is examined under homogeneous deformation. In particular, the materials under consideration are augmented neo-Hookean models with a function that accounts for the existence of a unidirectional reinforcing. This function endows the material with its anisotropic character and is called a reinforcing model, which depends on a particular deformation invariant. The anisotropy introduced here penalizes deformations in the fiber direction (as in previous analyses) and, additionally, more general deformations. The mechanical response of the material model is analyzed under normal homogeneous deformations for which the fiber direction is a principal direction of both stress and deformation. It is shown that the response curves are monotonic for fiber extension and nonmonotonic for fiber compression. The response of the material is also examined under plane shearing deformations in a plane containing the fiber reinforcement. It is shown that the shear stress in the shearing direction may be negative for positive shears. In this case, the shearing direction does not coincide with either the fiber direction or the perpendicular to the fiber direction. The behavior of the invariant considered is also examined and it is shown that under off-fiber shear deformations it may be non-convex depending on the direction of shear relative to the fiber direction.
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