Incompatibility and a simple gradient theory of plasticity

In the continuum theory, at finite strains the crystal lattice is assumed t o distort only elastically during plastic flow, while generally the elastic distortion itself is not compatible with a single-valued displacement fiel d. Lattice incompatibility is characterized by a certain skew-symmetry prop erty of the gradient of the elastic deformation field, and this measure can play a natural role in nonlocal theories of plasticity. A simple constitut ive proposal is discussed where incompatibility only enters the instantaneo us hardening relations. As a result, the incremental boundary value problem for rate-independent and rate-dependent behaviors has a classical structur e and rather straightforward modifications of standard finite element progr ams can be utilized. Two examples are presented in this paper: one for size -scale effects in the torsion of thin wires in the setting of an isotropic J(2) flow theory and the other for hardening of microstructures containing small particles embedded in a single crystal matrix. (C) 2001 Published by Elsevier Science Ltd.