AUSTIN, Texas -- Comparing bumps in a rug to boxes dragged across the floor and to earthquake fault zones, researchers at The University of Texas at Austin have developed new calculations to demonstrate that the mechanics of friction can be the same, no matter what the size of the materials involved.
Their work, published Sept. 20 in the journal Nature, could be used to improve understanding of the dynamics of earthquakes.
The authors are Dr. Michael Marder, of the Center for Nonlinear Dynamics, and Dr. Eric Gerde, a recent graduate who worked at the Texas Institute for Computational and Applied Mathematics. The research centers on "self-healing cracks" that have been postulated for some time, but had been plagued by mathematical paradoxes that Marder and Gerde have overcome.
"The need to understand the operation of friction in detail may be greatest in the context of geophysics, where it determines the onset of earthquakes and the heat they produce," said Marder, a professor in the Department of Physics.
By starting with a description of surfaces in contact at the atomic scale and employing multi-scale analysis, the researchers were able to provide a detailed picture of how objects can slide over one another, as when a box slides across a floor.
"We used this to demonstrate the existence of self-healing cracks that have been postulated to solve geophysical paradoxes," Marder said.
Like a bump on a rug, a self-healing crack refers to the temporary gap between a solid surface and another solid surface that allows one area to slide over the other. In sliding of rigid objects, the self-healing crack moves so rapidly it is hard to detect, and the motion and heat it produces can be interpreted as coming from ordinary friction.
"The most intriguing thing about friction is that it is proportional to the force pushing two objects together -- but it is independent of the size of the area in contact," Marder said. "The idea of the self-healing crack provides a new way to see why this should be so."
The researchers said they expect further experiments will demonstrate the same principles operate at many different scales -- ranging from books sliding across tables to massive scales such as Earth's tectonic plates.
Researchers at the Center for Nonlinear Dynamics study complex dynamics, instabilities, chaos and pattern formation in chemical, biological, solid, fluid and granular systems. Their findings underline the fact that diverse systems exhibit remarkably similar, sometimes even universal, behavior.
Marder is involved in a variety of theoretical, numerical experimental investigations. They range from studies of plasticity to experiments on sand ripples at the sea bottom. He specializes in the mechanics of solids, particularly the fracture of materials, and has developed analytical methods that explain the origin of fracture instability in crystals.
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