3.7 MeshDomains Section¶
The MeshDomains section assigns various physical attributes to the element sets of the mesh. For each of the Elements sections in the Mesh section, define a SolidDomain, ShellDomain, or BeamDomain section, depending on whether the elements are solid, shells, or beams (or trusses). Each domain also requires a material name that defines the material properties of the domain.
SolidDomain Section¶
Use the SolidDomain section to define a solid domain. This section takes the following parameters:
name The name of the element set (defined via an Elements section). This element set must only contain solid elements.
mat The name of the material that will be assigned to this domain
type (optional) the specific formulation used for this domain.
The optional type attribute can be added to specify a specific solid formulation. If omitted, FEBio will determine the proper domain type by inspecting the material and element types used. However, users can explicitly set the type attribute. The following solid domain types are defined. If the domain type is specified explicitly, the user must make sure that the assigned material is compatible with the domain type. (For instance, you cannot assign a biphasic material to an elastic-solid.)
| type | Description |
|---|---|
| elastic-solid | standard solid formulation (default for most materials) (1,2) |
| three-field-solid | A three-field formulation used for modeling (nearly) incompressible materials. (default for uncoupled materials) |
| rigid-solid | Rigid solid domain. (default for rigid materials.) |
| udg-hex | uniform deformation gradient hex formulation |
| sri-solid | Formulation that uses a selective reduced integration rule |
| remodeling-solid | Formulation used for elastic remodeling problems. |
| elastic-mm-solid | Formulation used for multi-scale domains. (requires the “micro-material”) |
| ut4-solid | Uniform nodal strain tetrahedron. (3) |
| biphasic-solid | The standard formulation for biphasic domains. |
| biphasic-solute-solid | The standard formulation for biphasic-solute domains. |
| multiphasic-solid | The standard formulation for multiphasic domains. |
| triphasic-solid | The standard formulation for triphasic domains (deprecated, use multiphasic-solid instead). |
| fluid-3D | The standard formulation for fluid domains. |
| fluid-FSI-3D | The standard formulation for fluid-FSI domains. |
Comments:
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For the elastic-solid domain, the elem_type attribute can be specified to further specialize the quadrature rule. The values of the rule depend on the specific element type. The tables below show the available integration rules for the different element types. The values marked with an asterisk (*) are the default.
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For the hex8 element, the following values are defined.
| hex8 | Description |
|---|---|
| HEX8G8* | Gaussian integration using 2x2x2 integration points. |
| HEX8G6 | Alternative integration rule for bricks using 6 integration point |
- For the hex20 element, the following values are defined.
| hex20 | Description |
|---|---|
| HEX20G8* | Gaussian integration using 2x2x2 integration points. |
- For the tet4 element, the following values are allowed.
| tet4 | Description |
|---|---|
| TET4G1* | Gaussian integration rule using one integration point. |
| TET4G4 | Gaussian integration rule using 4 integration points. |
- For the tet10 element, the following integration rules are supported.
| tet10 | description |
|---|---|
| TET10G4 | Gaussian integration rule using 4 integration points |
| TET10G8* | Gaussian integration rule using 8 integration points |
| TET10GL11 | Gauss-Lobatto integration rule using 11 integration points |
The Lobatto integration rule differs from a regular Gauss integration rule in that it includes the vertices of the tetrahedral element. The Lobatto11 integration rule uses the 10 tetrahedral nodes, plus one integration rule located at the center of the element.
- For the tet15 element, the following integration rules are defined.
| tet15 | description |
|---|---|
| TET15G8 | Gaussian integration rule using 8 integration points |
| TET15G11 | Gaussian integration rule using 11 integration points |
| TET15G15* | Gaussian integration rule using 15 integration points |
- For the penta15 element, the following values are defined.
| penta15 | Description |
|---|---|
| PENTA15G8* | Gaussian integration using 2x2x2 integration points. |
- The “solid-elastic” defines the parameters secant_stress and secant_tangent. When, specified, the formulation will use a secant approximation of the corresponding variable. When setting secant_stress is set to 1, the stress is calculated from a secant approximation that uses the material's strain-energy density. Similarly, when secant_tangent is specified, the material tangent is approximated using the PK2 stress.
3.The ut4-solid is a special formulation for tetrahedral elements that uses a nodally-averaged integration rule, as proposed by Gee et al 1. This formulation requires additional parameters. To override the default values, use the following alternative syntax:
<SolidDomain name="Part1" type="ut4-solid" mat="material1">
<alpha>0.05</alpha>
<iso_stab>0</iso_stab>
</SolidDomain>
The alpha parameter defines the amount of “blending” between the regular tet-contribution and the nodally integrated contribution. The value must be between 0 and 1, where 0 means no contribution from the regular tet and 1 means no contribution from the nodally averaged tet. The _iso_stab _parameter is a flag that chooses between two slightly different formulations of the nodally integrated tet. When set to 0, the stabilization is applied to the entire virtual work, whereas when set to 1 the stabilization is applied only to the isochoric part. See the FEBio Theory Manual for a detailed description of this formulation.
ShellDomain Section¶
Use the ShellDomain section to define a shell domain. This section takes two parameters:
name The name of the element set (defined via an Elements section). This element set must only contain shell elements.
mat The name of the material that will be assigned to this domain
type (optional) the specific shell formulation
Similar to solid domains, the particular shell formulation can be requested via the type attribute. If omitted, FEBio will determine the formulation from the material and shell element types. If specified explicitly, the user must ensure that the correct material is assigned to the domain. The following shell domain types are available.
| type | Description |
|---|---|
| elastic-shell | standard shell formulation (default for most materials) (1) |
| three-field-shell | A three-field formulation used for modeling (nearly) incompressible materials. (default for uncoupled materials) |
| rigid-shell | Rigid shell domain. (default for rigid materials.) |
| elastic-shell-old | The “old” shell formulation, used in FEBio version 2.0 and older. |
| elastic-shell-eas | Enhanced-Assumed-Strain shell; an alternative shell formulation for incompressible shells. |
| elastic-shell-ans | Assumed-Natural-Strain shell; an alternative shell formulation for incompressible shells. |
| biphasic-shell | The standard formulation for biphasic shell domains. |
| biphasic-solute-shell | The standard formulation for biphasic-solute shell domains. |
| multiphasic-shell | The standard formulation for multiphasic shell domains. |
The default shell thickness can be specified as a parameter of the ShellDomain section.
<ShellDomain name="skin">
<shell_thickness>0.01</shell_thickness>
</ShellDomain>
If the shell thickness parameter is not specified, the initial shell thickness is set to zero, and it is assumed that the actual shell thickness is specified in the MeshData section.
BeamDomain Section¶
Beam and trusses can be defined with the BeamDomain section. This tag takes the following attributes.
name This is the name of the part to which this domain will be assigned. The part is defined via a named Elements section.
mat The name of the material that will be assigned to this domain.
type The specific formulation that will be used.
The particular beam formulation that can be assigned is listed below.
| type | Description |
|---|---|
| linear-truss | A linear truss formulation. |
| elastic-truss | An extension of the linear-truss formulation that allows the use of standard FEBio materials (EXPERIMENTAL!) |
| linear-beam | A linear beam formulation. |
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Gee, M.W.; Dohrmann, C.R.; Key, S.W.; Wall, W.A.. "A uniform nodal strain tetrahedron with isochoric stabilization." Int. J. Numer. Meth. Engng, pp. 429-443 (2009). ↩