We study the asymptotic properties of fracture strength distributions of disordered elastic media by a combination of renormalization group, extreme value theory, and numerical simulation. We investigate the validity of the 'weakest-link hypothesis' in the presence of realistic long-ranged interactions in the random fuse model. Numerical simulations indicate that the fracture strength is well described by the Duxbury-Leath-Beale (DLB) distribution which is shown to flow asymptotically to the Gumbel distribution. We explore the relation between the extreme value distributions and the DLB type asymptotic distributions, and show that the universal extreme value forms may not be appropriate to describe the non-universal low-strength tail.
We study the failure of disordered materials by numerical simulations of the random fuse model. We identify emergent patterns of localized damage prior to catastrophic failure by statistically averaging the density of damage around the eventual failure nucleation point. The resulting pattern depends on fracture density and obeys the same scaling relations as would be expected for the stress field generated by a critical crack nucleating in a finite, disorder-free effective medium of varying size. The growth of this critical crack absorbs preexisting clusters according to a well-defined scaling relation. Unfortunately, in single model runs such precursory signals are not obvious. Our results imply that reliable and accurate prediction of failure in time-independent, microscopically brittle random materials in a real case is inherently problematic, and degrades with system size.
We study the connection between sliding friction and the phase behavior of a simple rigid bead-necklace model of a liquid crystal (LC) lubricant layer confined between two parallel plates. The dynamics is dependent on competing LC ordering mechanisms, including the direction of sliding, and an applied (electric) field. Together with temperature and an applied pressure, determining whether the lubricant is in a fluidlike isotropic state or in a layered in-plane nematic state, such ordering is found to control the frictional properties of the lubricant. Our extensive molecular dynamics simulations reveal in a detailed manner how friction can be controlled via applied fields. The results are expected to help in designing novel strategies to develop lubricants with dynamically controllable properties.
The strength of quasibrittle materials depends on the ensemble of defects inside the sample and on the way damage accumulates before failure. Using large-scale numerical simulations of the random fuse model, we investigate the evolution of the microcrack distribution as the applied load approaches the fracture point. We find that the distribution broadens mostly due to a tendency of cracks to coalesce in a way that increases with system size. We study how the observed behavior depends on the disorder present in the sample and relate the results with fracture size effects.
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