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We present a detailed study of rectilinear shear deformation in the frameworkof orthotropic nonlinear elasticity, under Dirichlet and mixed-boundaryconditions. We take a slab made of a soft matrix, reinforced with two familiesof extensible fibers. We consider the case where the shear occurs along thebissectrix of the angle between the two privileged directions aligned with thefibers. We show that if the two families of parallel fibers are mechanicallyequivalent, then only smooth solutions are possible, whereas if the mechanicaldifferences among the two families of fibers is pronounced, then strainsingularities may develop. We determine the precise conditions for theexistence of such singular solutions for the standard reinforcing orthotropicmodel. We then extend our findings to some orthotropic models of interest inbiomechanical applications, and we discuss the possible relevance of thesingular solutions to biomechanics.

Inhomogeneous shear of orthotropic incompressible non-linearly elastic solids: singular solutions and biomechanical interpretation