TET4TOTET10 option in *ELEMENT_SOLID
Ricardo Azevedo
Ron Ge
T.Kim Parnell, PhD, PE
Dear Ricardo,
References and notes with tetrahedron review comments:
tetrahedron elements
Tetrahedron elements are generally stiffer than hexahedron elements in incompressible
regimes, e.g., plasticity. The stiff behavior is most evident in bending modes. Use fine
meshing to minimize the stiff behavior.
elform=10 (1 point - 4-node linear tetrahedron) has resolved the issues of the degenerated/
collapsed elements (elform=1). It is a simple, fast, solid element that has proven to be very
useful in modeling low density foams that have high compressibility. If a tetrahedron is
needed, this element should be used instead of the collapsed solid element since it is, in
general, considerably more stable in addition to being much faster. This formulation is
however more prone to locking than elform=4.
The displacement field for the 4-node linear tetrahedron is linear while the strain field is
constant.
elform=13 (1 point nodal pressure tetrahedron) has no volumetric locking under plastic
flow conditions. This element formulation is automatically assigned when 3D R-adaptivity
is invoked for bulk forming/forging simulations.
From the following presentations:
Erhart, T., "Review of Solid Element Formulations in LS-DYNA: Properties, Limits,
Advantages, Disadvantages", 2011 Developer Forum, Stuttgart-Filderstadt, Germany,
October, 2011.
• For complex solid structures, tetrahedron elements are generally employed; elform=4,
10, 13, 16, or 17 are the available options (any of these formulations are preferable to
using degenerate elform=1 tetrahedrons). elform=16/17 are the most accurate tetra-
hedrons; however, not arbitrarily suited for large strains (due to limitation on the strain
increment). elform=13 needs a finer mesh, yet well suited for large strains (need to
check if desired material model is supported).
• For metals or plastics, with moderate strains, use elform=4, 13, 16, or 17.
• For rubber materials, with incompressible, large strains, use elform=13.
• For bulk metal forming problems, use elform=13 with 3D r-adaptivity.
Schmied, C., and Erhart, T., "Updated Review of Solid Element Formulations in LS-DYNA
Properties, Limits, Advantages, Disadvantages", 15th German LS-DYNA Forum, Bamberg,
Germany, October, 2018.
From LS-DYNA User’s Manual:
14. 1-Point Nodal Pressure Tetrahedron: Type 13. Element type 13 is identical to type 10
but includes additional averaging of nodal pressures, which significantly decreases the
chance of volumetric locking. Therefore, it is well suited for applications with income-
pressible and nearly incompressible material behavior, such as rubber materials or ductile
metals with isochoric plastic deformations (e.g. bulk forming). Compared to the standard
tetrahedron (type 10), a speed penalty with a maximum of 25% can be observed. For im-
plicit simulations, all material models supported for type 10 are also supported for this
element, while for explicit currently material models *MAT_001, 003, 006, 007, 015, 024,
027, 077, 081, 082, 089, 091, 092, 098, 103, 106, 120, 123, 124, 128, 129, 181, 183, 224,
225, and 244 are fully supported. For other materials this element behaves like the type
10 tetrahedron. Type 13 tetrahedral elements that use two different material models
should not share nodes because the nodal pressure averaging will cause spurious energy.
An exception to this rule is if the different materials have the same bulk modulus.
19. 1-Point Tetrahedron: Type 60. Aside from including additional averaging of element
volumetric locking, element type 60 is identical to type 10. In contrast to type 13, type
60 averages the normal stress between two adjacent elements, so nodes can be shared
between the different materials with different bulk modulus. Currently, this element
supports explicit analysis but is still under development for implicit simulations.
*CONTROL_SOLID
TET13K - Set to 1 to invoke a consistent tangent stiffness matrix for the pressure
averaged tetrahedron (type 13). This feature is available only for the implicit integrator
and it is not supported in the MPP/MPI version. This element type averages the volu-
metric strain over adjacent elements to alleviate volumetric locking; therefore, the
corresponding material tangent stiffness should be treated accordingly. In contrast to
a hexahedral mesh where a node usually connects to fewer than 8 elements, tetrahedral
meshes offer no such regularity. Consequently, for nonlinear implicit analysis matrix
assembly is computationally expensive, so this option is recommended only for linear
or eigenvalue analysis to exploit the stiffness characteristics of the type 13 tetrahedron.
Another presentation:
Stelzmann, U., "Die Grosse Elementbibliothek in LS-DYNA - Wann nimmt man was?"
28th CADFEM Users' Meeting, Aachen, Germany, November 2010.
http://www1.beuth-hochschule.de/~kleinsch/Expl_FEM/2010_Elementbibliothek_LSDyna_Cadfem.pdf
-------------------------------------------------
A note that I have shared to another user to a similar question.
Automatic Node Generation. The option TET4TOTET10 automatically converts 4 node
tetrahedron solids to 10 node quadratic tetrahedron solids. Additional mid-side nodes are
created which are shared by all tetrahedron elements that contain the edge. The user node
ID’s for these generated nodes are offset after the largest user node ID defined in the input
file.
When defining the *SECTION_SOLID keyword, the element type must be specified as
either 16 or 17 which are the 10-noded tetrahedrons in LS-DYNA. Mid-side nodes created
as a result of TET4TOTET10 will not be automatically added to node sets that include the
nodes of the original tetrahedron. So, for example, if the tetrahedrons are to have an initial
velocity, velocity initialization by part ID or part set ID using *INITIAL_VELOCITY_
GENERATION is necessary as opposed to velocity initialization by node set ID using
*INITIAL_VELOCITY.
The option H8TOH20/H8TOH27 provides the same functionality for converting 8-node to
20-node/27-node elements.
If *ELEMENT_SOLID defines 4-noded tetrahedrons, you can easily convert to 10-noded
tetrahedrons using the command *ELEMENT_SOLID_TET4TOTET10.
Likewise, I am assuming:
If *ELEMENT_SOLID defines 8-noded hexahedron input, you can easily convert to 27-
noded hexahedrons using the command *ELEMENT_SOLID_H8TOH27. It is my under-
standing that *SECTION_SOLID would still be using 8-noded input (elform=2).
If you use *SECTION_SOLID with elform=24, then you would use *ELEMENT_SOLID
with three lines of input (define all 27 nodes) per element.
Perhaps this presentation may be of some help:
Teng, H., “Recent Advances on Higher Order 27-Node Hexahedral Elements in LS-DYNA”,
14th International LS-DYNA Users Conference, Dearborn, Michigan, June, 2016.
-------------------------------------------------
Some timing information for a simple cantilever problem with a uniform
constructed mesh that may be of interest:
element element characteristic time normalized
formulation nodes/type element step run time
(elform) (hex-tet) length (Le) (dt) (nrt)
------------------------------------------------------------------
1 8-node hex V/Amax 1.75e-5 1.0
1 4-node tet hmin 1.02e-5 6.0
4 4-node tet 0.850 hmin 8.66e-6 14.5
10 4-node tet hmin 1.02e-5 2.0
13 4-node tet hmin 1.02e-5 2.3
16 10-node tet 0.3889 hmin 3.96e-6 27.0
17 10-node tet V/Amax 3.40e-6 48.0
360 elements in hex mesh and 1800 elements in tet mesh
Another timing study is given in the paper above.
-------------------------------------------------
Sincerely,
James M. Kennedy
KBS2 Inc.
November 5, 2020
James M. Kennedy
Dear Ricardo,
Comments offered in the following two presentations agree with your observation.
• For complex solid structures, tetrahedron elements are generally employed; elform=4,
10, 13, 16, or 17 are the available options (any of these formulations are preferable to
using degenerate elform=1 tetrahedrons). elform=16/17 are the most accurate tetra-
hedrons; however, not arbitrarily suited for large strains (due to limitation on the strain
increment). elform=13 needs a finer mesh, yet well suited for large strains (need to
check if desired material model is supported).
• For metals or plastics, with moderate strains, use elform=4, 13, 16, or 17.
• For rubber materials, with incompressible, large strains, use elform=13.
• For bulk metal forming problems, use elform=13 with 3D r-adaptivity.
Erhart, T., "Review of Solid Element Formulations in LS-DYNA: Properties, Limits,
Advantages, Disadvantages", 2011 Developer Forum, Stuttgart-Filderstadt, Germany,
October, 2011.
Schmied, C., and Erhart, T., "Updated Review of Solid Element Formulations in LS-DYNA
Properties, Limits, Advantages, Disadvantages", 15th German LS-DYNA Forum, Bamberg,
Germany, October, 2018.
--------------------------------------------------
Some other comments found in the literature:
Tetrahedral elements can fit better complex geometry. However, when you integrate the
shape functions with points of Gauss it is less accurate than hexahedral elements. In addition,
one of the factors that determines the quality of your mesh is the distortion of your elements.
The reason for this lays on the mapping from real to natural space of integration. To sum up,
if your geometry is simple, the best option is to mesh it with hexahedral elements. If it is not
possible (curved geometries, accute angles or similar) then go with tetrahedal but controlling
the distortion of the elements.
Hexahedra meshes are economic with the number of elements because the same degrees of
freedom (or for 8 nodes) for one Hexaedron corresponds to six Tetrahedra. It is obvious that
increasing the number of elements will not increase the size of the global finite element matrices
but the computations for one hexahedron are generated also for six tetrahedra. This step has to
be compared in cpu time in order to state if it is interesting to use hexahedra than constant strain
tetrahedra knowing that curved or linear hexahedra use Gauss intergration points to generate the
element characteristics (stiffness, mass, ..) and tetrahedra use exact formula without any integra-
tion to get the same characteristics. Researchers have always used tetrahedra elements because
they fit very well arbitrary shaped geometries with their simple computations.
--------------------------------------------------
Interesting comments shared here:
East, J., “Finite Element Model Development with LS-PrePost”, DSO-2018-07, Dam Safety
Technology Program, Department of the Interior, Bureau of Reclamation, Technical Service
Center, Denver, Colorado, May, 2018.
https://www.usbr.gov/ssle/damsafety/TechDev/DSOTechDev/DSO-2018-07.pdf
--------------------------------------------------
p.s. A run time performance of the various tetrahedron formulations and mesh density
study for a three-point bending specimen simulation was shared:
Mohapatra, S., "Evaluation of Advanced Element Formulations for Failure Prediction of
Highly Complex 3D-Printed Parts", 11th European LS-DYNA Users Conference, Salzburg,
Austria, May, 2017.
--------------------------------------------------
Sincerely,
James M. Kennedy
KBS2 Inc.
November 9, 2020
--
You received this message because you are subscribed to the Google Groups "LS-DYNA2" group.
To unsubscribe from this group and stop receiving emails from it, send an email to ls-dyna2+u...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/ls-dyna2/4caf5b97-8927-490f-8557-ba145fdb9528n%40googlegroups.com.