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In this work we do not consider fracture or brittle behavior. Following Argon et al. [16, 18], we use the term "shear band" widely to represent quasilinear (in 2D) [or quasiplanar (in 3D)] objects where shear strains are localized. The narrowest ones are slips composed of dislocation pairs.
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6 from expansion (2.6). This suggests room of improvement for our nonlinear strain theory.
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0 are the shear and bulk viscosities, respectively [50].
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If ρ is included as a dynamic variable, ρ obeys the continuity equation ∂p/∂t = -∇ (ρv) and the right hand side of Eq. (2.17) should be replaced by ρ[∂/∂t + v · ∇]v. Then the self-consistency relation (2.20) is kept to be valid. For large strains of order 1 this generalization is needed.
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59
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-1) appears in the range a≲r≲ℓl. The lower bound is provided by nonlinear elasticity theory. This slip energy also follows from Eq. (3.11).
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60
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In 2D, the glide direction is along the Burgers vector b, and the climb direction is perpendicular to b [1,2].
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The Peierls potential energy depends on the ratio of the atomic spacing across the glide plane and the magnitude of the Burgers vector [1, 2, 44, 45]. As a result, the critical stress causing dislocation motion (Peierls stress) can strongly depend on the orientation of the glide plane with respect to the crystal axes.
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