Calculate contact area of indentation

Dear all,

I was trying to calculate the contact area Ac when performing a nano-indentation by applying a sphere indenter on the sample with the command “fix 1 all indent $k sphere …”.

Here is my idea: (1)calculate the distance r from the center of atom i to the sphere center; (2)if r<R (sphere radius), then this atom is considered to be a contacting atom with the indenter; (3)determine all the contacting atoms based on the above criterion; (4)finally, the contact area could be calculated by this formula: Ac = Npira^2, where N the number of contacting atoms, ra the radius of the atom.

But I don’t know how to realize this idea by using LAMMPS command? I guess “fix” or “compute” might be used and looked up these two commands, but still not very clear about how to write the scripts.

Can someone give me a hint or any advice on it? What’s more, are there any other methods to calculating the contact area of indentation?

Thank you in advance.

Best,

Weilin

Dear all,

I was trying to calculate the contact area Ac when performing a
nano-indentation by applying a sphere indenter on the sample with the
command "fix 1 all indent $k sphere ...".

Here is my idea: (1)calculate the distance r from the center of atom i to
the sphere center; (2)if r<R (sphere radius), then this atom is considered
to be a contacting atom with the indenter; (3)determine all the contacting
atoms based on the above criterion; (4)finally, the contact area could be
calculated by this formula: Ac = N*pi*ra^2, where N the number of contacting
atoms, ra the radius of the atom.

there are a few of problems with this approach.

- what about the gaps between the atoms?
- what about atoms that are not fully exposed to the indenter?
- since both the atoms and the indenter are not based on hard spheres,
what is the *exact* radius?
- and even if you define a radius, you are looking at essentially a
fractal property, since surface on the atomic scale is rough and not
flat and thus its magnitude depends a lot on the resolution.

now, this doesn't mean that there is no way to get an approximate
surface area. and i have two possible strategies.
a) you can use a "solvent accessible surface area" tool used in
biosimulations that uses a specific probe of a given radius. with the
proper adjustments, this should be adaptable to your needs
b) you define (i.e. program) a compute that places a grid of points
with suitable resolution on your indenter surface (again, you have to
make a properly justifiable choice of radius here) and then choose a
suitable atom radius and count which of those gridpoints overlap with
one ore more atoms. since each grid point is associated with a
spherical surface segment, the summation will give you an
approximation of the contact surface.

but keep in mind, in a strict sense, this property only makes sense
macroscopically.
axel.