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.
In several material models you will find settings named
Use mixed formulation
or
Compressibility
, by which you can introduce a mixed formulation.
Use a mixed formulation when the material data is such that the deformation is close to being incompressible. For an isotropic elastic 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.
For more details, see
Mixed Formulation
in the theory chapter.
