Dear all
As known, tangent modulus is the gradient of stress with respect to strain. this mechanical continuum property, likewise the atomic stress, can be defined with explicit formulation in the atomic domain.

I wonder that LAMMPS can calculate this important parameter for atoms?

First develop stress-strain response by doing tensile simulation of your atomistic model with LAMMPS. From the stress-response, you can get whatever modulus/properties you want.

Thanks for your response, but i I do not mean to determine the
stress-strain relation with numerically calculation the gradient of stress
with changing the small value of strain. in the other word, i need to
determine the tangent modulus for each atom likewise the stress.

as i mentioned in previous email, determination the tangent modulus for
each of the atoms, likewise the stress tensor, can be performed on the
basis of derivative of inter-atomic potential which is reported in
literature. i wonder that LAMMPS can possibly do that?

Thanks for your response, but i I do not mean to determine the
stress-strain relation with numerically calculation the gradient of stress
with changing the small value of strain. in the other word, i need to
determine the tangent modulus for each atom likewise the stress.

as i mentioned in previous email, determination the tangent modulus for
each of the atoms, likewise the stress tensor, can be performed on the
basis of derivative of inter-atomic potential which is reported in
literature. i wonder that LAMMPS can possibly do that?

i don't think so. it would have to be programmed. what LAMMPS *can* do is
referenced in the manual.
as a general rule, there are no features added to LAMMPS without adding the
corresponding documentation to the manual.