Elasticity and topological defects: a common thread between soft and hard materials

A unified kinematical basis for the description of topological defects in soft or hard materials, based on a characterization of integrability of specified distortion fields will be discussed. This kinematics will be embedded into a continuum mechanical framework consistent with non-negative dissipation. The resulting model will be illustrated through select examples of disclination statics and dynamics in nematic liquid crystals and, separately, experimentally observed grain and subrain boundaries in a hard metal.