Lattice incompatibility and a gradient theory of crystal plasticity. (English) Zbl 0963.74010

Summary: In the finite-deformation continuum theory of crystal plasticity, the lattice is assumed to be distorted 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.


74C20 Large-strain, rate-dependent theories of plasticity
74E15 Crystalline structure
Full Text: DOI


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