A continuum code investigation of stress integration using exact and approximate material rotation
Abstract
The accuracy of the Zaremba-Jaumann-Noll stress rate (referred to as the Jaumann Stress Rate) used in various continuum mechanics codes is investigated using two realistic warhead formation problems that involve isotropic plasticity, large deformations, and large rigid body rotation. It was demonstrated in the literature for simple problems that, although the Jaumann Stress Rate is objective (i.e., under superimposed rigid body rotation, it transforms in like manner as the stress or strain rate), it is not kinematically consistent because it uses the anti-symmetric part of the velocity gradient tensor to approximate rigid body rotation. A theoretically correct approach would use an objective stress rate that is kinematically consistent via the use of the exact rigid body rotation rate. It is shown that, although the Jaumann Stress Rate is sufficiently accurate for gross deformation, inspection of the stress-strain details show kinetical errors. The computational expense of using an exact rotation rate is shown to be insignificant.
- Publication:
-
NASA STI/Recon Technical Report N
- Pub Date:
- November 1992
- Bibcode:
- 1992STIN...9331013D
- Keywords:
-
- Continuum Mechanics;
- Error Analysis;
- Plastic Properties;
- Rigid Structures;
- Rotating Bodies;
- Stress-Strain Relationships;
- Warheads;
- Isotropic Media;
- Plastic Deformation;
- Strain Rate;
- Tensors;
- Structural Mechanics