From: Rick Link <rick@combdyn2.com>
Subject: Re: Cauchy stress
Date: Tue, 15 Jun 1999 16:50:29 -0300
Newsgroups: sci.math.num-analysis

> Simi wrote:
> >
> > I have been told Cauchy Stress caclulation is highly accurate for large
> > displacements.
> >
> > Does anyone know of an example where I could see the mathematics for the
> > calculations for streses in a 2D finite element based on the Cauchy
> > principle?

For large strains and rotations, 2 formulations are quite popular:

1) 2nd Piola-Kirchoff stresses and Green-Lagrange strains - the equations of
motion are linearized, and Cauchy stresses are calculated from the 2nd P-K
ones, because 2nd P-K stresses have very little meaning.  2nd P-K stresses
include the effect of rigid body rotation of the material.

2)  Jaumann stress rates and velocity strain tensors - the Jaumann stress
rates include the effect of the rigid body rotation of the material.

If straight Cauchy stresses are used, incorrect results will be obtained,
because the effect of rigid body rotations is not included.

Rick.