Abstract
In the continuum theory, at finite strains the crystal lattice is assumed to distort only elastically during plastic flow, while generally the elastic distortion itself is not compatible with a single-valued displacement field. Lattice incompatibility is characterized by a certain skew-symmetry property of the gradient of the elastic deformation field, and this measure can play a natural role in nonlocal theories of plasticity. A simple constitutive proposal is discussed where incompatibility only enters the instantaneous hardening relations. As a result, the incremental boundary value problem for rate-independent and rate-dependent behaviors has a classical structure and rather straightforward modifications of standard finite element programs 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.
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