# How to calculate: J-integral, strain energy release rate, and crack size?

Hello Everyone,

I am a beginner using the LAMMPS for modeling crack propagation in 2D materials. In my simulation, I would like to calculate the J-integral, the crack size, and the strain energy release rate at each time step. I developed an input file which is mainly similar to the crack example of the LAMMPS. I will be so thankful if someone help me with the following questions:

1- How can I calculate the j-integral at each time step using the LAMMPS?

2- How can I calculate the strain energy release rate at each step using the LAMMPS?

Note, as you may know, the strain energy release rate is the amount of energy dissipated during fracture per unit of newly created fracture surface area.

3- What is the best technique to accurately find the crack size? Does the LAMMPS calculate it (if yes, please let me know the command)? or Do I need to visualize the simulation results in a visualization software and then find the crack size?

I looked in the LAMMPS’ manual and some web searches. I saw some partial answers for my questions which are not clear for me at all. Unfortunately, because I am a new user, I cannot implement them as well. I really appreciate it if someone, please, writes and explains the command lines that I need to add into my input file for calculating those three parameters.

Thank you so much in advance.

Hello Everyone,

I am a beginner using the LAMMPS for modeling crack propagation in 2D
materials. In my simulation, I would like to calculate the J-integral, the
crack size, and the strain energy release rate at each time step. I
developed an input file which is mainly similar to the crack example of the
LAMMPS. I will be so thankful if someone help me with the following
questions:

1- How can I calculate the j-integral at each time step using the LAMMPS?

2- How can I calculate the strain energy release rate at each step using the
LAMMPS?

Note, as you may know, the strain energy release rate is the amount of
energy dissipated during fracture per unit of newly created fracture surface
area.

3- What is the best technique to accurately find the crack size? Does the
LAMMPS calculate it (if yes, please let me know the command)? or Do I need
to visualize the simulation results in a visualization software and then
find the crack size?

I looked in the LAMMPS' manual and some web searches. I saw some partial
answers for my questions which are not clear for me at all. Unfortunately,
because I am a new user, I cannot implement them as well. I really
appreciate it if someone, please, writes and explains the command lines that
I need to add into my input file for calculating those three parameters.

as a new user, you should not start with your research problem, but
need to learn how to perform basic simulations with LAMMPS first.
nobody is likely to do what you are asking for, as that is essentially
doing *your* work for *and* giving you a customized personal tutorial.
if you are unsure about how to do your research, please discuss with
your adviser, as that is the job of your adviser to advise you on
doing your research.

if you have specific questions to specific commands or how they are
implemented and so on, people are happy to help.
the fact that you are new to LAMMPS is no reason why you should be
entitled to get your work done by somebody else. you need to learn the
tools of the trade just like everybody else has. this doesn't happen
over night and this only works in steps.

axel.

All of the quantities you are asking about
are complicated values, depending on things
like surface area of a crack, etc. LAMMPS
will dump snapshots as often as you wish.
If you can figure out how to compute the
values you want from a snapshot of atom
positions, that is the first step. Then
you might figure out how to get LAMMPS
to do portions of the calculation for you,
but likely you would have to add new options
to LAMMPS to compute the values you
are asking about.

Steve

Thanks Steve and Luis for the response.

Let me please rephrase my question. The strain energy release rate (SER) is differential of total energy (U+K-W) with respect to the crack length (SER=d(U+K-W)/dl). Where, U is the total strain energy due to mechanical deformations (also named potential energy); K is the total kinetic energy; W is the total work of the external work; and l is the crack length. I’m somehow familiar how to calculate the U and K but I don’t know how to calculate the W as well as the crack length. Furthermore, I am not what is the potential energy that the LAMMPS calculates by ‘compute all pe’ command. Is it the potential due to the mechanical deformations or the potential due to the charges?

Luis,

Thanks for the file. Now J-integral calculation makes sense to me. Thanks.

Thanks everyone.

The LAMMPS potential energy is simply

whatever the pair style you define computes for

the interactions of all the atoms with each other.

The crack length is something that it is easy

to look at a visual snapshot (at least in 2d) and

say, there’s the crack, it’s this long. But automating

that to have LAMMPS compute it for you is non-trivial.

How would you compute it, if all you had was a dump

snapshot of atom coords?

Steve