FE is a widely acknowledged and popular tool for complex problems. However, computation at nano-scale is more complicated where strain or strain gradient may come at even smaller scale. Other issue like capturing accurate van der Waals interaction is also difficult to achieve where inter atomic equilibrium distance is just fraction of nanometer. Molecular mechanics(MM) or Molecular dynamics (MD) simulations are the other ways to capture those issues. However, their computational efficiency is also limited. Now, how can we resolve those issues with this existing FE formulation?
Angelo Oñate
Thanks for your response. I understand that MD simulation is better in terms of accuracy at nanoscale. However, computational time, geometric domain size and efficiency are other important issues. Even a powerful PC finds it hard to simulate few millions of atoms or molecules. FEM is very good at macro or micro scale. However, to bridging between micro and nano or even smaller scale using FE simulation is still challenging.
Look at the problem from another angle: FEM intrinsically deals with field theories, that is, your fundamental quantity is a function of spatial coordinates (e.g., strain) that you can resolve (within your theory) to an arbitrarily high resolution.
Now as you approach the nanoscale, you start to notice that matter is not a continuous thing, but consists of atoms with space in-between. And then you get into trouble, not because FEM breaks down, but because the underlying field theory and its input parameters breaks down (what is the strain in the middle between two iron atoms?). So you either try to do something smart and think hard about how to build up a useful field theory (then you can use FEM), or you ditch it and do something else like MD.
Ulf Lorenz Thanks for your valuable comment. Still we are searching a way to accommodate nano-scale issues in micro scale or macro scale simulation. As an example, for nano-composites, one of the critical part is modeling of interface region where nano-scale effect is prominent for getting an accurate force transferring mechanism.
And I apologize if my answer is not as useful because I am outside my immediate field of experience. It is sometimes hard to guess the level and accurate direction of a given question.
Multi-scale analysis is then probably the answer, though I can caution from what I have heard and experienced with even smaller systems that embedding different theories is prone to artifacts or parametrization-dependent results.
Ulf Lorenz I think your answer is quite logical and your effort is appreciable. Now a days research overlaps one discipline to another and the area is so vast and deep that computational effort is to be in the wide range to coop with the physical problems and unknown situations.
Though I am not from this field, yet I find it very interesting topic. Pl continue to enlighten us more
I guess it depends on "How much Nano".
In nano scale properties are defined as Atoms or Molecules, which are "Discrete" Points.
The fundamental of FEM is to Fit Continuous Function within an element. Which is completely different than Discrete points like atoms or molecules.
But if you have enough large structure that can be modeled as a continuous medium , then it should work.
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