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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.

MSC:

74C20 Large-strain, rate-dependent theories of plasticity
74E15 Crystalline structure
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