Chaotic particle dynamics above and below yield in a 2D jammed material

Amorphous materials, often fail catastrophically, just beyond yield. This is a problem not just in design engineering (harnessing high strength glasses without the chance of ruinous breakdowns), but also in predicting the failure of non-constrained, natural systems (averting damage caused by mudslides). The yielding transition has previously been observed in both experiments and simulations to present via the emergence of specific particle trajectories, known as reversibly or irreversibly plastic. Here we present detailed quantification of Lagrangian properties (displacement lengths, arc-lengths, and enclosed area) of experimentally obtained particle trajectories for the purpose of illuminating where plasticity occurs in space and time both above and below yield. Our findings suggest plastic trajectories, both reversible and irreversible, predominantly occur in specific regions as a function of the strain amplitude, but not time. These findings imply that the yield transition is of the first order and that mean field and thermodynamic models are attainable. In this direction, we introduce a non-dimensional measure of plastic dissipation that applies both above and below yield and captures the rheological yield point.