An analytic nonlinear theory models plastic dipoles in amorphous solids to derive shear band formation via instability in the displacement field, with expressions for band profiles and a critical stress from the Hessian of an energy functional.
In that case we can estimate α 4 (f ′)4 ≈ B 4 (f 2 − f 2 0 )2
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Analytic Nonlinear Theory of Shear Banding in Amorphous Solids
An analytic nonlinear theory models plastic dipoles in amorphous solids to derive shear band formation via instability in the displacement field, with expressions for band profiles and a critical stress from the Hessian of an energy functional.