# Construction of Berkovich Indenter

Hi LAMMPS users,

I am trying to study the nano-indentation behaviour of Copper single and poly-crystal. I want to create a berkovich indenter. Previous question and documentation doesnot give enough information about normal vectors used to create three different planes required for construction of indentor. Taking (0,0,0) as the indentation tip, can anyone help in providing the approach to obtain normal vectors of three planes.

Yours Sincerely
Ayush Suhane
Department of Metallurgical Engineering
IIT(BHU), Varanasi
India

Hi LAMMPS users,

I am trying to study the nano-indentation behaviour of Copper single and
poly-crystal. I want to create a berkovich indenter. Previous question and
documentation doesnot give enough information about normal vectors used to
create three different planes required for construction of indentor. Taking
(0,0,0) as the indentation tip, can anyone help in providing the approach to
obtain normal vectors of three planes.

you have to be a bit more specific about what kind of strategies you
have tried already. no manual or documentation will have the perfect
answer for all specific projects, but most of the time you as a uses
will have to develop a strategy to approach doing the (complex) task
by a combination of simpler tasks.

more importantly, have you made some estimates as to how large a
system you will have to set up in order to get meaningful answers,
since it looks to me you want to mimic a macroscopic experiment.

one hint that i can give from the little information you provide:
please keep in mind that you can build geometries by defining a volume
and filling it with atoms, but you can also fill some volume and then
take some atom in some partial volume away. hopefully, this kind of
approach inspires you to look for strategies on your own.

axel.

If you want an atom-based indenter, then
you simply need to create atoms that fill some
volume inside the geometry bounded by the 3 planes.

You can do this with region intersect, and use

3 planes as the sub-regions that intersect.

If you mean an idealized indenter like fix indent
does with a sphere, then you would have to add a

new fix, or an option to that fix, that computed forces

on all atoms due to the idealized indenter and its
current position.

Steve

Thanks Steve,

I understand I have to use region intersect the corresponding 3 planes to get the required volume. My problem is how to get those 3 plane normals to define the region plane.

Thanks Steve,

I understand I have to use region intersect the corresponding 3 planes to
get the required volume. My problem is how to get those 3 plane normals to
define the region plane.

http://lammps.sandia.gov/doc/region.html

Thanks Axel,

I think there is some misunderstanding. Thing is to construct a complex shape, say a berkovich indenter here, there are two options :
1). To create a volume and delete atoms as per requirement.
2). Subdivide the complex shape into simpler regions, here 3 planes, and use their intersection.

Now, in both these cases, plane needs to be defined, which requires a point on the plane and normal vector of the plane. I have read the region command documentation thoroughly. Problem is I couldn’t calculate the normal vectors required for any plane. Using first method described above, I started of removing atoms from a cube, but couldnot proceed above one plane. I tried calculating the normal vectors of other planes given the plane of first plane, but couldn’t till now.

I require the normal vectors specifically, as I have the points of the three planes as the indenter tip, or approach to find these will also be appreciated.

Thanks

Yours Sincerely
Ayush Suhane

Thanks Axel,

I think there is some misunderstanding. Thing is to construct a complex
shape, say a berkovich indenter here, there are two options :
1). To create a volume and delete atoms as per requirement.
2). Subdivide the complex shape into simpler regions, here 3 planes, and
use their intersection.

Now, in both these cases, plane needs to be defined, which requires a point
on the plane and normal vector of the plane. I have read the region command
documentation thoroughly. Problem is I couldn't calculate the normal
vectors required for any plane. Using first method described above, I
started of removing atoms from a cube, but couldnot proceed above one plane.
I tried calculating the normal vectors of other planes given the plane of
first plane, but couldn't till now.

well, this is a geometry/math problem, not a lammps problem.

i suggest you talk to somebody local that has more experience in
elementary spatial geometry or pick up a suitable text book or contact
a mailing list focusing on such things.

axel.

You’re pushing your luck here. Finding the normal vectors for the indenter is not a LAMMPS Q but a math one. Only someone who’s done it before can give the answer.

Carlos

You're pushing your luck here. Finding the normal vectors for the indenter
is not a LAMMPS Q but a math one. Only someone who's done it before can give

it is rather elementary vector algebra. i remember having to deal with
that in middle school. it basically need a piece of paper and a
pencil, a suitable text book and some common sense to solve these
issues. that is not too much to ask of a scientist, i think.

on top of that, since LAMMPS supports "instant visualization" via the
dump image command, it is possible to even do this in a more empirical
fashion for mathematically challenged people.

axel.

I agree. All you need to do is find the vectors running along the edges (summit centered at the origin). The cross products of consecutive pairs will give you the normals. The 2d projection of the indenter forms an equilateral triangle thus here you have how to get the x,y components. For the z one all you need is to use the corresponding angle between the z axis and the triangular faces. This can be done easily using the indenter geometry data. Now is up to you to put the pieces together.

For \$100/hr (1.5 hr min charge) I’ll do it for you.

Carlos

I agree. All you need to do is find the vectors running along the edges
(summit centered at the origin). The cross products of consecutive pairs
will give you the normals. The 2d projection of the indenter forms an
equilateral triangle thus here you have how to get the x,y components. For
the z one all you need is to use the corresponding angle between the z axis
and the triangular faces. This can be done easily using the indenter
geometry data. Now is up to you to put the pieces together.
For \$100/hr (1.5 hr min charge) I'll do it for you.

no price dumping, please. i usually ask for \$150/h in cases like these
(and that is really cheap already).

I suggest you take Axel up on his offer; probably the best \$12.50 you will spend!

Just saved my pocket money!!! Thanks to all.