Mixed Formulation
Nearly incompressible materials can cause numerical problems if only displacements are used in the interpolating functions. Small errors in the evaluation of volumetric strain, due to the finite resolution of the discrete model, are exaggerated by the high bulk modulus. This leads to an unstable representation of stresses, and in general to underestimation of the deformation because spurious volumetric stresses might balance also applied shear and bending loads.
When the Pressure formulation is selected in the Use mixed formulation list, the negative volumetric stress pw is treated as an additional dependent variable. The resulting mixed formulation is also known as u-p formulation. This formulation removes the effect of 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 a finite-element sense) to the original pressure calculated from the strains.
Select this setting when the material data is close to incompressibility. For an isotropic material, this happens when Poisson’s ratio approaches 0.5.
The mixed formulation is useful not only for linear elastic materials but also for elastoplastic materials, hyperelastic materials, and viscoelastic materials.
The order of the shape function for the auxiliary pressure variable should be one order less than that for the displacements. Thus, it is not recommended to use linear elements for the displacement variables in the domains, where the mixed formulation is turned on. Also note that some iterative solvers do not work well together with mixed formulation because the stiffness matrix becomes indefinite.