Lattice incompatibility and a gradient theory of crystal plasticity

In the finite-deformation, continuum theory of crystal plasticity, the latt ice is assumed to distort only elastically, while generally the elastic def ormation itself is not compatible with a single-valued displacement field. Lattice incompatibility is shown to be characterized by a certain skew-symm etry property of the gradient of the elastic deformation field, and this me asure can play a natural role in a nonlocal, gradient-type theory of crysta l plasticity. A simple constitutive proposal is discussed where incompatibi lity only enters the instantaneous hardening relations, and thus the increm ental moduli, which preserves the classical structure of the incremental bo undary value problem. (C) 2000 Elsevier Science Ltd. All rights reserved.