fedoo.weakform.StressEquilibrium.incompressibility

property StressEquilibrium.incompressibility

Method used to avoid volumetric locking.

Nearly incompressible materials lead to volumetric locking with the standard displacement formulation. The available methods are:

  • None (default): standard displacement formulation.

  • “auto”: use the most suitable method for each type of element (currently “mean_dilatation” where available). The standard formulation is kept with a warning for elements without any available method (“tri3”, “tet4”, …).

  • “mean_dilatation”: mean dilatation method (B-bar method based on a volume weighted projection of the dilatation). Equivalent to a mixed formulation with element-wise discontinuous pressure and dilatation that are eliminated at the element level: the problem only contains the displacement and the tangent matrix remains symmetric. One pressure value per element is used for “quad4”, “hex8”, “wed6”, “tri6” and “tet10” elements, and a linear pressure for “quad8”, “quad9”, “hex20”, “wed15” and “wed18” elements. The number of gauss points should be higher than the number of pressure values (no effect with reduced integration). Available in small strain and with the updated lagrangian method. The geometric_stiffness attribute should be set to True to get the consistent tangent matrix in finite strain.

  • “sri”: legacy small-strain B-bar method where the dilatation is evaluated at the element center, for “quad4” and “hex8” elements only. Its use with updated-Lagrangian finite strains emits a warning because the formulation is not consistent.

  • “fbar”: F-bar method where the volume change is evaluated at the element center. The consistent non symmetric tangent matrix is used for “quad4” and “hex8” elements (not available for ‘2Daxi’ and with the total lagrangian method). In small strain, it reduces to a center-based B-bar volumetric correction.

This attribute should be defined before the creation of the associated assembly. Elements with constant strain (“tri3”, “tet4”) or reduced integration elements are not improved by these methods: see fedoo.weakform.StressEquilibriumMixed or fedoo.weakform.StressEquilibriumRI. Incompressibility treatments are ignored with the plane-stress assumption.