[Pw_forum] Kind of Stress tensor

[stefano de gironcoli]

the stress in the code is defined as the derivative of the energy per 
unit volume with respect to infinitesimal deformations
sigma_alpha,beta = 1/Omega partial E / partial epsilon_alpha,beta
for a deformation such that
r_alpha -> r'_alpha = r_alpha + sum_beta epsilon_alpha,beta r_beta
it is symmetric in alpha,beta because the antisymmetric components of 
the deformation (describing rotations) do not change the energy.

If I understand correctly the stress definitions 
(https://en.wikipedia.org/wiki/Stress_measures) for infinitesimal 
deformations they are all the same
because J=1, F=I, dn_0=dn, ... etc

If you are considering finite deformations the stress is the derivative 
taken w.r.t. the present deformed configuration so I think must be the 
Cauchy stress because the code does not know you want to take another 
configuration as reference.
Therefore, should be something like  S = J (F^-1) sigma  (F^-1)^T

HTH

stefano



On 17/02/2017 16:27, Mahdi Faghihnasiri wrote:
> Dear all,
>
> I know If I set tstress=.true. the stress tensor will be computed and
> printed. but What's the kind of the Stress Tensor QE dose print? for example Cauchy,
>   true, Kirchhoff, PK2, ...
> I am trying to calculate second Piola–Kirchhoff (PK2) stresses with QE. Any suggestions or comments are appreciated.
>
> Sincerely
> Mahdi
> *Mahdi FaghihNasiri*
> Department of Physics
> Shahrood University of Technology
> Shahrood,Iran**
>
>
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