Abstract
We focus on the probability distribution function (PDF) where are the measured strain intervals between plastic events in a athermal strained amorphous solids, and measures the accumulated strain. The tail of this distribution as (in the thermodynamic limit) scales like . The exponent is related via scaling relations to the tail of the PDF of the eigenvalues of the plastic modes of the Hessian matrix which scales like . The numerical values of or can be determined easily in the unstrained material and in the yielded state of plastic flow. Special care is called for in the determination of these exponents between these states as increases. Determining the dependence of the PDF can shed important light on plasticity and yield. We conclude that the PDF's of both and are not continuous functions of . In slowly quenched amorphous solids they undergo two discontinuous transitions, first at and then at the yield point to plastic flow. In quickly quenched amorphous solids the second transition is smeared out due to the nonexisting stress peak before yield. The nature of these transitions and scaling relations with the system size dependence of are discussed.
- Received 16 September 2015
DOI:https://doi.org/10.1103/PhysRevE.92.062302
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