Rheology and Shear Band Suppression in Particle and Chain Mixtures

Using numerical simulations, we consider an amorphous particle mixture which exhibits shear banding, and find that the addition of even a small fraction of chains strongly enhances the material strength, creating pronounced overshoot features in the stress-strain curves. The strengthening occurs in the case where the chains are initially perpendicular to the shear direction, leading to a suppression of the shear band. For large strain, the chains migrate to the region where a shear band forms, resulting in a stress drop. The alignment of the chains by the shear bands results in a Bauschinger-like effect for subsequent reversed shear. Many of these features are captured in a simple model of a single chain being pulled through a viscous material. Our results are also useful for providing insights into methods of controlling and strengthening granular materials against failure

Elasticity with Arbitrarily Shaped Inhomogeneity

A classical problem in elasticity theory involves an inhomogeneity embedded in a material of given stress and shear moduli. The inhomogeneity is a region of arbitrary shape whose stress and shear moduli differ from those of the surrounding medium. In this paper we present a new, semi-analytic method for finding the stress tensor for an infinite plate with such an inhomogeneity. The solution involves two conformal maps, one from the inside and the second from the outside of the unit circle to the inside, and respectively outside, of the inhomogeneity. The method provides a solution by matching the conformal maps on the boundary between the inhomogeneity and the surrounding material. This matching converges well only for relatively mild distortions of the unit circle due to reasons which will be discussed in the article. We provide a comparison of the present result to known previous results.Comment: (10 pages, 10 figures

Memory switching due to thermal noise in amorphous solids subject to cyclic shear

The discovery that memory of particle configurations and plastic events can be stored in amorphous solids subject to oscillatory shear has spurred research into methods for storing and retrieving information from these materials. However, it is unclear to what extent the ability to store memory is affected by thermal fluctuations and other environmental noises, which are expected to be relevant in realistic situations. Here, we show that while memory has a long lifetime at low temperatures, thermal fluctuations eventually lead to a catastrophic loss of memory, resulting in the erasure of most or all of the stored information within a few forcing cycles. We observe that an escape from the memory-retaining state (limit cycle) is triggered by a change in the switching of plastic events, leading to a cascade of new plastic events that were not present in the original limit cycle. The displacements from the new plastic events change the particle configuration which leads to the loss of memory. We further show that the rate of escaping from a limit cycle increases in a non-Arrhenius manner as a function of temperature, and the probability of staying in a limit cycle decays exponentially with an increase in the shearing frequency. These results have important implications for memory storage since increasing the temperature offers a means of effectively erasing existing memories and allowing for the imprinting of new ones that can then be stored for a long time at low temperatures.Comment: 7 pages, 9 figure