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Timescale Multiscaling in Atomistic Simulations of Experimental Nanostructures
We all know most atomistic simulations in nanomechanics are performed on ideal materials that are not produced in laboratory and most experiments in nanomechanics are performed on materials that cannot be analyzed using atomistic simulations. Atomistic simulations indeed have a great capability in revealing a material's behavior with only constitutive law being used is that in the form of interatomic potential. The strain rate in atomistic simulations is of the order of 100000000 per sec which has not yet been achieved in any experiment or in a practical application. In this paper:"Nanometer to micron scale mechanics of [100] silicon nanowires using atomistic simulations at accelerated time steps" Phys. Status Solidi A, 1–9 (2011) / DOI 10.1002/pssa.201026578" http://onlinelibrary.wiley.com/doi/10.1002/pssa.201026578/abstract we have resolved timescale and length scale issues in simulating non-equilibrium deformation of nanowires with experimental sizes. Fundamental question that is answered is that can we simulate deformation of an experimentally sized nanostructure at experimental strain rates? Needless to say there are flaws which need working. However we believe this is first such work which addresses multiscaling in length aswell as time scales using classical atomistic simulations to resolve constitutive behavior of materials.We hope this method can be extended to resolve issues in discrete dislocation dynamics types of schemes for truely timedependent coupling in various multiscale problems. We also have another work on polycrystalline thin film failure using the same method. We'll post it as it becomes available. Right now its is going through author proof procedures. "Nanometer to Micron Scale Atomistic Mechanics of Silicon Using Atomistic Simulations at Accelerated Time Steps Hansung Kim; Vikas Tomar" to appear in ASCE-Journal of Nanomechanics and Micromechanics
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The most difficult part of multiscale modeling is the non-self-similarity between different scales. There are always different intrinsic characteristic scales governing different phenomena. These characteristic scales will be missing in any kinds of self-similar framework. Coarsening only works when the sub-scale doesn't matter.
So your uniform corsening (self-similar) scheme may only work for predicting of bulk properties ( there are no intrinsic scales), but not for others. For example, your 54.3 supercell will give (if it can) a dislocation structure with Burgers vector roughly on the order of the larttice constant (54.3), which is meaningless. For real lattice (lattice constant is 5.43), there is only one intrinsic scale that matters, the lattice constant or the real Burgers vector. Self-similarity will not apply for this case and many other cases.
Its only upper bound study
As i have pointed out..its only upper bound study. This study can very well predict all defects if instead of 10 times larger cell one only has 2 times and then 3 times lrger cell.
one will have to use an approach similar to that used in adaptive FEM mesh sizes..using smaller size lattices where defects are generated and gradually using larger sized lattices as one goes to regions where there are no defects. For timescaling one can use multi-time step methods.
Based on this i disagree with what you said. for lattice sized burger vector alttice sized cell will be used and to propagate that to higher length scales higher sized cells.
all cells will work in an adaptive manner. just a matter of numerical implementation. (and some ersearch support)
It is fine if you only use
It is fine if you only use this as a local coarsening scheme and use hybrid cells (multiscales), or you use a globally-uniform coarsening scheme but interpret the result as a upper bound result. At least this scheme remains the discrete nature of lattice and conserves the topology of lattice. I commented only on the globally-uniform coarsening scheme itself when it is applied to studies of non-bulk properties.
It will be very interesting if you can extend your study to multiscale case. I am looking forward to seeing your new results in the future.
extending to multiscale
yes..that is the next shot..we want to use classical atomistics to solve a crystal plasticity problem...looking for someone with pockets right now.