  We introduce a continuum model for a fibre reinforced material in which the
reference orientation of the fibre may evolve with time, under the influence of
external stimuli. The model is formulated in the framework of large strain
hyperelasticity and the kinematics of the continuum is described by both a
position vector and by a remodelling tensor which, in the present context, is
an orthogonal tensor representing the fibre reorientation process. By imposing
suitable thermodynamical restrictions on the constitutive equation, we obtain
an evolution equation of the remodelling tensor governed by the Eshelby torque,
whose stationary solutions are studied in absence of any external source terms.
It is shown that the fibres reorient themselves in a configuration that
minimises the elastic energy and get aligned along a direction that may or may
not be of principal strain. The explicit analysis of the Hessian of the strain
energy density allows us to discriminate among the stationary solutions, which
ones are stable. Examples are given for passive reorientation processes driven
by applied strains or external boundary tractions. % Applications of the
proposed theory to biological tissues, nematic or magneto-electro active
elastomers are foreseen.
