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Mechanics of Two-dimensional Media: Carbon Nanotubes and Fluid Membranes
Marino Arroyo, April 24, 2008 Mechanics of two-dimensional media: carbon nanotubes and fluid membranes The study of solids and fluids in domains that are very small in one dimension, such as shell theory, is classical in continuum mechanics. Intrinsically two-dimensional media are less common, even though interesting systems can be understood in this way. This talk will focus on two examples, one dealing with a solid and one with a fluid. (Part A) Carbon nanotubes (CNTs). We present a realization of hierarchical modeling, starting from atomistic models to develop a continuum mechanics crystal elasticity model for curved lattices. This continuum model grants very efficient simulations of multi-million atom systems, which allow us to characterize the nonlinear elastic response of multi-walled CNTs. We identify a unified law consisting of two distinct power-law regimes in the energy-deformation relation, described in terms of elastic constants, a critical length-scale and an anharmonic energy-deformation exponent. The mechanical response of MWCNTs is found to be strongly size-dependent. Based on these observations, we propose a mesoscopic beam model with non-convex curvature energy, which develops stressed phase mixtures composed of smoothly bent sections and rippled sections in agreement with observations. (Part B) Lipid membranes are the most prominent example of amphiphilic fluid membrane. We focus on the two dimensional motion of the membrane constituents on the curved, time-evolving surface of the membrane. We study the dynamics of the formation of a protruding bud in a fluid membrane, as a model problem for physiological processes on the cell wall, and find that the viscous drag caused by the shear of the membrane constituents is the dominant dissipation mechanism governing the dynamics of liquid membranes in a wide parameter range.
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