A couple of interesting papers in the latest issue of PNAS.
- Localized and extended deformations of elastic shells, A Vaziri and L Mahadevan.
The dried raisin, the crushed soda can, and the collapsed bicycle inner tube exemplify the nonlinear mechanical response of naturally curved elastic surfaces with different intrinsic curvatures to a variety of different external loads. To understand the formation and evolution of these features in a minimal setting, we consider a simple assay: the response of curved surfaces to point indentation. We find that for surfaces with zero or positive Gauss curvature, a common feature of the response is the appearance of faceted structures that are organized in intricate localized patterns, with hysteretic transitions between multiple metastable states. In contrast, for surfaces with negative Gauss curvature the surface deforms nonlocally along characteristic lines that extend through the entire system. These different responses may be understood quantitatively by using numerical simulations and classified qualitatively by using simple geometric ideas. Our ideas have implications for the behavior of small-scale structures.
- A liquid-crystal model for friction, C H A Cheng, L H Kellogg, S Shkoller, and, D L Turcotte
Rate-and-state friction is an empirical approach to the behavior of a frictional surface. We use a nematic liquid crystal in a channel between two parallel planes to model frictional sliding. Nematic liquid crystals model a wide variety of physical phenomena in systems that rapidly switch between states; they are well studied and interesting examples of anisotropic non-Newtonian fluids, characterized by the orientational order of a director field d(x,t) interacting with the the velocity field u(x,t). To model frictional sliding, we introduce a nonlinear viscosity that changes as a function of the director field orientation; the specific choice of viscosity function determines the behavior of the system. In response to sliding of the top moving plane, the fluid undergoes a rapid increase in resistance followed by relaxation. Strain is localized within the channel. The director field plays a role analogous to the state variable in rate-and-state friction.
By the way, for those of you who are so inclined, Vaziri and Mahadevan’s paper also talks about symmetry-breaking elastic bifurcations, and the first figure in the paper is that of a plastic bottle indented by a sharp pen!
Tags: deformation of elastic shells, friction, liquid-crystals, symmetry-breaking elastic bifurcations
