Yielding Transitions in Amorphous Materials

Amorphous materials form a part of a wide array of common materials, including foams, emulsions, colloidal and metallic glasses and polymeric systems. Many amorphous materials exhibit yielding transitions from a solid-like to a fluid-like state under shear, and characterising and predicting these transitions is of key importance in a variety of industrial and biological applications. We study the yielding of amorphous materials in three separate studies. First, we use a thermal fluidity model to explore the yielding transitions of an amorphous material under a shear startup protocol and categorise the yielding transitions as either brittle or ductile. We find that ductile and brittle yielding both occur in systems with a stress overshoot as a function of strain, with no need for an overhang, in contrast to recent claims in the literature. Second, we use the Soft Glassy Rheology (SGR) model and a thermal elastoplastic model (EPM) to study slow fatigue followed by sudden catastrophic failure of amorphous materials subjected to a large amplitude oscillatory shear strain protocol. We find that both models display delayed yielding, in which there is a significant stress drop after many cycles. We fit the number of cycles before yielding to functions of the relevant physical parameters. In the SGR model, we find a critical amplitude below which the yielding is delayed but insignificant, and in the EPM we find a temperature-dependant critical amplitude at which the yielding cycle diverges. Third, we attempt to derive a continuum model of epithelial tissue rheology. We present several model variants, and compare them to published Self-Propelled Voronoi (SPV) model simulations of epithelial rheology. While we are unable to derive a model that fully captures all of the features seen in the SPV Model, we do identify several necessary ingredients of an eventual successful model.