  We propose a framework to model elastic properties of polycrystals by
coupling crystal orientational degrees of freedom with elastic strains. Our
model encodes crystal symmetries and takes into account explicitly the strain
compatibility induced long-range interaction between grains. The coupling of
crystal orientation and elastic interactions allows for the rotation of
individual grains by an external load. We apply the model to simulate uniaxial
tensile loading of a 2D polycrystal within linear elasticity and a system with
elastic anharmonicities that describe structural phase transformations. We
investigate the constitutive response of the polycrystal and compare it to that
of single crystals with crystallographic orientations that form the
polycrystal.
