UC Santa Barbara
Shear-transformation-zone theory of yielding in athermal amorphous materials.
- Author(s): Langer, JS
- et al.
Published Web Locationhttps://arxiv.org/abs/1501.07228v2
Yielding transitions in athermal amorphous materials undergoing steady-state shear flow resemble critical phenomena. Historically, they have been described by the Herschel-Bulkley rheological formula, which implies singular behaviors at yield points. In this paper, I examine this class of phenomena using an elementary version of the thermodynamic shear-transformation-zone (STZ) theory, focusing on the role of the effective disorder temperature, and paying special attention to scaling and dimensional arguments. I find a wide variety of Herschel-Bulkley-like rheologies but, for fundamental reasons not specific to the STZ theory, conclude that the yielding transition is not truly critical. In particular, for realistic many-body models with short-range interactions, there is a correlation length that grows rapidly but ultimately saturates near the yield point.
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