  When a block made of an elastomer is subjected to large shear, its surface
remains flat. When a block of biological soft tissue is subjected to large
shear, it is likely that its surface in the plane of shear will buckle
(apparition of wrinkles). One factor that distinguishes soft tissues from
rubber-like solids is the presence -- sometimes visible to the naked eye -- of
oriented collagen fibre bundles, which are stiffer than the elastin matrix into
which they are embedded but are nonetheless flexible and extensible. Here we
show that the simplest model of isotropic nonlinear elasticity, namely the
incompressible neo-Hookean model, suffers surface instability in shear only at
tremendous amounts of shear, i.e., above 3.09, which corresponds to a 72
degrees angle of shear. Next we incorporate a family of parallel fibres in the
model and show that the resulting solid can be either reinforced or strongly
weakened with respect to surface instability, depending on the angle between
the fibres and the direction of shear, and depending on the ratio E/mu between
the stiffness of the fibres and that of the matrix. For this ratio we use
values compatible with experimental data on soft tissues. Broadly speaking, we
find that the surface becomes rapidly unstable when the shear takes place
"against" the fibres, and that as E/mu increases, so does the sector of angles
where early instability is expected to occur.
