Lattice incompatibility and a gradient theory of crystal plasticity

In the finite-deformation, continuum theory of crystal plasticity, the lattice is assumed to distort only elastically, while generally the elastic deformation itself is not compatible with a single-valued displacement field. Lattice incompatibility is shown to be characterized by a certain skew-symmetry property of the gradient of the elastic deformation field, and this measure can play a natural role in a nonlocal, gradient-type theory of crystal plasticity. A simple constitutive proposal is discussed where incompatibility only enters the instantaneous hardening relations, and thus the incremental moduli, which preserves the classical structure of the incremental boundary value problem. (C) 2000 Elsevier Science Ltd. All rights reserved.