Nearly incompressible 3 field domain - element type

[wzaylor]

Hi,

I've been working with the FEBio code, and I noticed that for a nearly-incompressible material the domain varies if a hex8 or a tet10 element is used. For example, when I run a model with a 'trans iso Mooney-Rivlin' material and hex8 elements, the stiffness matrix is formulated using functions from FEBioMech/FE3FieldElasticSolidDomain.cpp. Conversely, if the same model is run using tet10 elements, the stiffness matrix is formulated using functions in FEBioMech/FEElasticSolidDomain.cpp.

Is there a reason the stiffness matrix formulation changes depending on the element type?

Please let me know if I can clarify anything.

Thank you for your help,
-Will

[ateshian]

Hi Will,

Linear elements (tet4, penta6, hex8) don't have enough nodal displacement degrees of freedom to enforce incompressibility at every integration point. That's why they lock when an incompressible (or nearly-incompressible) material model is used. The three-field formulation attempts to enforce incompressibility in an average sense over the entire element volume, instead of enforcing it at each integration point. See the book by Bonet and Wood (Nonlinear Continuum Mechanics for Finite Element Analysis, 1997, 2008) for an explanation of this method.

Quadratic elements don't suffer from the same limitation, so it is neither necessary nor beneficial to use the three-field formulation for these elements.

Best,

Gerard

[wzaylor]

Ok, thank you for the explanation!