  We investigate, in a fairly general setting, the limit of large volume
equilibrium Gibbs measures for elasticity type Hamiltonians with clamped
boundary conditions. The existence of a quasiconvex free energy, forming the
large deviations rate functional, is shown using a new interpolation lemma for
partition functions. The local behaviour of the Gibbs measures can be
parametrized by Young measures on the space of gradient Gibbs measures. In view
of unboundedness of the state space, the crucial tool here is an exponential
tightness estimate that holds for a vast class of potentials and the
construction of suitable compact sets of gradient Gibbs measures.
