Dear all
I'm going to evaluate the mechanical response (stress-strain profile) of some materials using molecular dynamics simulation. I found different strain rates result various Young modulus and failure strain. How could this happen? What is the correct strain rate?
If you want to obtain a quasi-equilibrium result, the answer is simply "infinitesimally close to zero". On the other hand, if you want to compare with experimental data, the "correct" strain rate would be the one used in the experiment.
For MD simulations (I assume you are using reactive force fields), both scenarios are generally prohibitive as they would require enormous CPU time. In principle, in fast rupture simulations your reaction coordinate will be quickly dragged from the material being "whole" to "broken", but other orthogonal degrees of freedom may not have sufficient time to relax. This means that in many pulling simulations, your system will follow a non-optimal pathway. If the system has more time to sample the configuration space, it will more often choose the low energy pathways. If you drag it too quickly, it will be forced to choose the high energy ones.
Now, for sufficiently small systems (that have relatively few degrees of freedom) it may suffice to perform a much slower simulation to obtain a good approximation of the actual values. If this is not the case, and if you want to remain rigorous in your approach, you can resort to non-equilibrium statistical mechanical models, e.g., based on the Bell model, and infer meaningful data from multiple pulling simulations. You can look up the paper in the link for a general discussion of some of the key ideas, such as the logarithmic dependence of the failure strain on the strain rate, or the relaxation of orthogonal degrees of freedom.
https://www.mpibpc.mpg.de/9556091/Kappel_2012_PhysRevLett_109_118304.pdf
If you want to obtain a quasi-equilibrium result, the answer is simply "infinitesimally close to zero". On the other hand, if you want to compare with experimental data, the "correct" strain rate would be the one used in the experiment.
For MD simulations (I assume you are using reactive force fields), both scenarios are generally prohibitive as they would require enormous CPU time. In principle, in fast rupture simulations your reaction coordinate will be quickly dragged from the material being "whole" to "broken", but other orthogonal degrees of freedom may not have sufficient time to relax. This means that in many pulling simulations, your system will follow a non-optimal pathway. If the system has more time to sample the configuration space, it will more often choose the low energy pathways. If you drag it too quickly, it will be forced to choose the high energy ones.
Now, for sufficiently small systems (that have relatively few degrees of freedom) it may suffice to perform a much slower simulation to obtain a good approximation of the actual values. If this is not the case, and if you want to remain rigorous in your approach, you can resort to non-equilibrium statistical mechanical models, e.g., based on the Bell model, and infer meaningful data from multiple pulling simulations. You can look up the paper in the link for a general discussion of some of the key ideas, such as the logarithmic dependence of the failure strain on the strain rate, or the relaxation of orthogonal degrees of freedom.
https://www.mpibpc.mpg.de/9556091/Kappel_2012_PhysRevLett_109_118304.pdf
Strain is quasi-equilibrium phenomena by definition, Sayyed. If You study dynamic, You study something else.
In molecular dynamics, mechanical results depends on the strain rate and it should be.
Usually, experimental strain rates are very high and if you will apply those rate in Molecular dynamics, you may lose some important infromation. secondly, at higher strain rate, bonds can break and this may be a reason for the simulation faliure. Hope this will help you, look for fig. 6
http://www.sciencedirect.com/science/article/pii/S0032386110008839#
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