When the Pressure formulation is selected in the
Use mixed formulation list, the volumetric stress
pw is treated as an additional dependent variable. The resulting mixed formulation is also known as a
u-p formulation. This formulation removes the effect of the volumetric strain from the original stress tensor, and replaces it with an interpolated pressure,
pw. A separate equation constrains the auxiliary pressure variable to make it equal (in an average sense) to the original pressure which is calculated from the strains.
When the Strain formulation is selected in the
Use mixed formulation list, the volumetric strain
εw is treated as an additional dependent variable.
When the Pressure formulation is selected for isotropic linear elastic materials, the stress tensor
s, computed directly from the strains, is replaced by a modified version:
where I is the unit tensor. The pressure
p is calculated from the stress tensor as
where K is the bulk modulus. Scaling by the bulk modulus is necessary, since typical values for the auxiliary pressure
pw are in the order of 10
6 to 10
9 Pa, while typical values for the displacement degrees of freedom are orders of magnitude smaller.
When the Strain formulation is selected for isotropic linear elastic materials, the auxiliary volumetric strain
εw is used instead of the auxiliary pressure
pw, and it is the set equal to the volumetric strain
εvol using the equation
The advantage of using the Strain formulation is that the values for the auxiliary strain
εw are of a similar order of magnitude as the displacement degree of freedom.