AEM faculty spotlight:
Imagine a city full of people. If one is trying to predict traffic flow for the future, large-scale observation and statistics are quite prudent. But to understand traffic flow, individual motivations need to be surveyed and understood. This is somewhat impractical city-wide. One must wonder if there is a happy medium or way to bridge the gap between individuals and population flow. This is analogous to a common problem in solid mechanics, and AEM Professor Ellad Tadmor has developed a theory to address it: the Quasicontinuum Method. This method allows for an efficient transition from large-scale, or continuum, calculations to progressively finer calculations until the movement of atoms is being determined. Below, Professor Tadmor discusses the Quasicontinuum Method and its implications for solid mechanics and designer materials.
What is the traditional method of modeling, and why try something novel?
The standard engineering practice is to use equations derived from continuum mechanics and thermodynamics to describe the behavior of materials and fluids, but this requires additional information about the properties of the material. These properties are obtained in an empirical fashion through a series of tests performed in a lab. This approach works extremely well – everything around you is built in this way. But it is limited. If someone wants to build a new structure, it may be ideal to design a material for that structure or to improve properties of existing materials. An engineer may also want to predict how the properties of an aging material will change over time. These are areas that empirical engineering is incapable of doing in a fundamental, predictive way. This is done on a trial-and-error basis.
Let’s say you have a metal and the metal has cracks in it. You want to know under what conditions, if any, the cracks would propagate, and whether a stronger metal could be made by adding impurities. If you were doing a purely continuum, large-scale simulation like people normally do, those properties would be inputs into the model, not results. You would have to guess some kind of a rule of how things break based on your experiments or some theory. It cannot really be a predictive model in any kind of fundamental sense. If you want to do something fundamental in this example you must consider what it means when a crack propagates – the atoms near the tip of the crack move apart dissipating the bonds holding them together. At the other end you say, fine, I’ll do my calculation with atoms. You use a computer to follow the Newtonian dynamics of each and every atom. The problem is that you can’t make a big enough system, it becomes too expensive. In one cubic centimeter of material, there’s something like 10^23 atoms. There is no computer on Earth that can predict things like that. The biggest supercomputers can do a few billion atoms for about a nanosecond. So under that paradigm, you can’t see a big enough picture for long enough to be useful.
Last Modified: Friday, 14-Oct-2011 13:17:44 CDT -- this is in International Standard Date and Time Notation