Jamming Transition And Rheology In Amorphous Solid

Phase transition is ubiquitous in our life, for example liquid-gas and liquid-solid transition. The phase transitions in equilibrium system have been well studied, even can be predicted quantitatively. However, there are so many unknowns in non-equilibrium system, like the transition from amorphous solids to liquids. Lots of systems can be described by this kind of transition, like glass transition, rheology of granular matter, traffic flow and so on. They share a common character:there is no big difference in structure between the states before and after the transition, but the mechanical and dynamical properties change significantly. To understand these phenomena, a simple model-Jamming transition has been proposed. There are three parameters in this model, density, temperature and shear stress. The amorphous solids turn into liquids by de-creasing the density, or increasing the temperature or shear stress.For purely repulsive systems, there is a special point called Point J in the jamming model. The jamming transition at point J has mixed characters of first and second order phase transitions. By increasing the density, we can see that potential, pressure, shear modulus and bulk modulus are increased from zero continuously, but the coordination number jumps suddenly at point J. To understand the jamming transition well, we must consider the influences of the other two parameters, temperature and shear stress. Our work concerns about the properties of point J from the perspective of shear, and show the evidence of the divergence of the correlation length indirectly.In addition, we developed a new method to find stable states that can resist the desired shear stress, we can then do the statistical average to the states with the same shear stress and measure the shear stress dependance of jammed state properties. We measured the potential, pressure, the distribution of interaction and the anisotropy of force network and found the differences between the ensemble of constant-shear-stress and quasi-static-shear. Besides these, our work showed that the force networks around the average force which is also the dividing line between the strong and weak force networks are asymmetry.Inspired by the experiments, we studied the behaviors of systems with short range attraction under the shear stress and find the same phenomena with experiments. And we defined three zones below point J, which are shear jamming, shear fragile and shear gelation.