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arXiv · 1501.07228

Shear-Transformation-Zone Theory of Yielding in Athermal Amorphous Materials

J. S. Langer
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Abstract

Yielding transitions in athermal amorphous materials 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, there is a correlation length that grows rapidly, but ultimately saturates near the yield point.

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J. S. Langer. 2015-05-25. Shear-Transformation-Zone Theory of Yielding in Athermal Amorphous Materials. https://arxiv.org/abs/1501.07228

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