Lecture 7 Element formulations 15.0 Release
Workbench LS-DYNA (ACT Extension) Training
Overview of Explicit Dynamic Elements •
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Each element type is valid for most of the material models and nonlinear options supported in ANSYS Workbench LS-DYNA. Some explicit element types have several different formulations. The default formulation is usually single point integration. Explicit dynamic elements have a linear displacement function, function, except for quadratic elements (with mid-nodes.) Extra shape functions and P-elements are not available in ANSYS Workbench LS-DYNA.
Overview of Explicit Dynamic Elements •
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Each element type is valid for most of the material models and nonlinear options supported in ANSYS Workbench LS-DYNA. Some explicit element types have several different formulations. The default formulation is usually single point integration. Explicit dynamic elements have a linear displacement function, function, except for quadratic elements (with mid-nodes.) Extra shape functions and P-elements are not available in ANSYS Workbench LS-DYNA.
Overview of Element Formulations: Solids If the discretized parts are relatively similar in geometric dimensions in three orthogonal directions, use Solid Elements
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Hexahedral solid elements •
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Tetrahedral solid elements •
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Approximate Gauss volume integration SCP: Standard Constant Pressure as pressure integration algorithm ANP: Average Nodal Pressure as pressure integration algorithm
Pentahedral solid elements •
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Can be used to replace the collapsed solid elements. Usually not recommended with the LS-DYNA solver. Although a warning message is shown during export, this does not affect the export process.
Overview of Element Formulations: Shell If the discretized parts have the relatively small geometric dimension in one of the three orthogonal directions, use Shell Elements
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Multiple formulations can be selected
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Can model both bending and membrane deformations
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Quadrilateral or Triangular element
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Thickness is a parameter (not modeled geometrically)
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Actual thickness can be rendered
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Time step is controlled by the element dimension, not by thickness. Thus shell elements can make thin-walled structures to have larger time step.
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Overview of Element Formulations: Beams If the discretized parts have the relatively large geometric dimension in one of the three orthogonal directions, use Beam Elements
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Can model both bending and axial deformations Only for the materials of elastic or elastic-plastic with kinematic hardening Cross-section is a parameter (not modeled geometrically) Actual cross section can be rendered Time step is controlled by the element length, not by the dimensions of cross-section. Thus beam elements can make slender structures to have larger time step.
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Reduced Integration Formulation •
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A reduced integration element is an element which has a minimum number of integration points. A reduced integration brick element has one integration point at its centroid. A reduced integration shell has one in-plane integration point, but still has multiple integration points through the thickness of the shell. Fully integrated elements are typical in implicit ANSYS. In ANSYS WORKBENCH LS-DYNA, fully integrated brick elements have eight integration points and fully integrated shells have four in-plane integration points (with multiple points through the thickness).
Reduced integration saves CPU time by minimizing element processing. Therefore, it is the default formulation most often used in ANSYS WORKBENCH LS-DYNA.
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… Reduced Integration Formulation •
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In addition to saving CPU time, single point integration elements are also extremely robust in large deformation. ANSYS LS-DYNA elements can undergo much greater deformations than standard ANSYS implicit elements. Two basic disadvantages of reduced integration elements are: – –
Deformations with zero energy modes are possible (Hourglassing). The accuracy of stress results is directly related to the number of the integration points.
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Hourglassing •
Hourglassing is a zero-energy mode of deformation that oscillates at a frequency much higher than the structure’s global response. Hourglassing modes result in stable mathematical states that are not physically possible. They typically have no stiffness and give a zigzag deformation appearance to a mesh. –
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Single-point (reduced) integration elements with linear displacement functions are prone to zero energy modes (hourglassing). The occurrence of hourglass deformations in an analysis can invalidate results and should always be minimized or eliminated. If the overall hourglass energy is more than 10% of the internal energy of a model, the results are suspect. Determining the level of hourglass energy can be found from LS-DYNA ASCII output files GLSTAT and MATSUM. In some cases, even an hourglass ratio of 5% can be considered excessive.
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… Hourglassing •
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Zero energy deformations for the one-point integrated solid element:
This mesh distortion produces no strain or volume change in the mesh. Hourglass control brings additional stiffness or viscous damping to minimize these non-physical, zero energy modes.
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… Hourglassing •
Minimizing hourglassing in ANSYS WORKBENCH LS-DYNA: –
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Avoid single point loads, which are known to excite hourglass modes. Since one excited element transfers the mode to its neighbors, point loads should not be applied. Try to apply loads over several elements as pressures, if possible. Refining the mesh often reduces hourglass energy, but a larger model corresponds to increased solution time and larger results files. Use fully integrated elements, which do not experience hourglassing modes. However, penalties in solution speed, robustness, and even accuracy may result, depending on the application. Alternatively, a few fully integrated “seed” elements may be dispersed through the mesh to minimize hourglassing. beams are not effected by hourglassing. The higher order tet element is not subject to hourglass modes, but it is not as robust as the lower order tet .
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… Hourglassing •
Minimizing hourglassing in ANSYS WORKBENCH LS-DYNA (continued) Globally add elastic stiffness to reduce hourglass energy. This can be done for the entire model by increasing the hourglassing coefficient in Hourglass Control defined in Analysis Settings: • Stiffness hourglass control is recommended for problems deforming with lower velocities (e.g., metal forming and crash).
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Care should be used when increasing the hourglassing coefficient. Values above 0.15 have been found to overstiffen the model’s response during large deformations and cause instabilities.
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… Hourglassing •
Minimizing hourglassing in ANSYS WORKBENCH LS-DYNA (continued) – Locally reduce hourglassing in high risk areas of a model without dramatically changing the model’s global stiffness. The added Hourglass Control by Body is used to apply hourglass control only to a specific material .
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LS-DYNA locally applies hourglass control on a Part ID basis (not on a material basis), so any Part with the specified material will have this hourglass control. LS-DYNA ID 5 is often used to reduce hourglassing.
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Control Hourglass Deformation •
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In order to avoid such hourglass instabilities, a set of corrective forces are added to the solution –
The corrective forces are called as Hourglass Damping
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Always recommended for reduced-integrated solid/shell elements
To specify Hourglass locally or Globally Recommend stiffness hourglass control, LS-DYNA ID=4, with hourglass coefficient QM = 0.03 for metal and plastic parts. Recommend viscosity-based hourglass control for foams and rubbers (LS-DYNA ID =2 or 3) or hourglass formulation 6 –
In soft materials, stiffness-based hourglass control causes overly stiff response even with a reduced hourglass coefficient.
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Control Hourglass Deformation Always check hourglass energy from Material output (MATSUM) and Global data (GLSTAT)
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The Hourglass Energy should be much less than the Internal Energy
If hourglass energy is very high, consider to
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Refine the mesh in your model
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Re-run the model in double precision
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Section : Properties & Formulations •
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The user can change the formulation of element using the following icon
Be carefull to check the compatibility of formulation with selected elements
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1st Order Tetrahedral Solid Elements 4-node elements with single point integration
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Primary use for transitions in HEX dominated meshes
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Advantages
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Simple, fast
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No need for hourglass control 3
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Too stiff for the applications involving large material deformation and motion
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Avoid the 4-node elements from the collapsed 8-node solid elements. Use tetrahedral solid elements because they are more stable and run much faster
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1st Order ANP Tetra Element 1st Order Tetra Element: ANP (Average Nodal Pressure)
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Enhanced tetra element, the default
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Overcomes volume locking problems
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Can be used as a majority mesh element
LS-DYNA Keyword: *SECTION_SOLID
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Element formulation option: ELFORM = 13
Well suited for applications with incompressible or nearly incompressible material behavior, i.e., rubber materials or ductile materials in bulk forming
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1st Order SCP Tetra Element 1st Order Tetra Element: SCP (Standard Constant Pressure)
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“Textbook” 4-node iso-parametric tetra elements
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Exhibit both volume and shear locking
To use SCP tetra elements
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Click on 1 point tetrahedron
LS-DYNA Keyword: *SECTION_SOLID
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Element formulation option: ELFORM = 10
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2nd Order Tetrahedral Solid Elements •
10-node elements with fully integration formulation
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Advantages –
Well suited for modeling irregular meshes (especially curved shapes)
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No need for hourglass control
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Take more CPU time than 1 st order tetra elements
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2nd Order Tetrahedral Solid Elements To introduce midside nodes to Tetra elements
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Click on Mesh
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Click on Patch Independent method
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Change the Element Midside Nodes from Use Global Setting or Dropped to Kept
LS-DYNA Keyword: *SECTION_SOLID
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Element formulation option: ELFORM = 16
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Element Formulations Can change the default element formulations as follows •
Right-click on Workbench LS-DYNA > Insert > Section –
Select the appropriate body to apply it to.
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Brick Elements Two main brick element formulations are available: •
Single point integrated solid (constant stress over the element) –
Default formulation
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Very fast and very robust for large element deformations
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Hourglass controls is typically needed to prevent hourglass modes
Fully integrated S/R solid (2x2x2 integration) –
Slower formulation, but has no hourglass modes
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Hex Integration Type = Exact has no effect
Both shear locking and volumetric locking (for high Poisson’s ratios) can occur, giving poor results
Accuracy more sensitive to element shape than for default formulation Generally not recommended
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Tetrahedral Elements 4-noded tets: •
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Considerably more elements are required to fill a volume with the same mesh density as bricks (6 – 10 times). Contact pressures are calculated correctly for all 4-noded tets. Very robust when elements become distorted. –
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Suitable for very large strain applications.
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Tet type 10 (LS-DYNA element type)
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Very fast but can be too stiff in bending
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Susceptible to volumetric locking, thus not suitable for plastic deformation or parts with incompressible materials.
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…Tetrahedral Elements Other options: •
1 point Nodal Pressure Tetrahedron –
Tet type 13
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Not susceptible to volumetric locking and more accurate in bending
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Good choice for plastic deformation or parts with incompressible materials.
S/R Quadratic Tetrahedron –
Tet type 4
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Contains 6 degrees-of-freedom per node (translations and rotations)
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No hourglass modes (5 integration points)
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Accurate in bending and not susceptible to volumetric locking
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Much slower than the other two options
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…Tetrahedral Elements 4 or 5 point 10-noded Tetrahedron • • • • •
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10-noded tetrahedral element with 4 or 5 integration points. Quadratic displacement behavior No hourglass modes Not accurate with contact For the same mesh density, the time step is ½ the size of a time step for a brick element because the distance between nodes is ½ as large. Very accurate but can generate very long run times. Not robust when elements get distorted during large strain analyses. Not recommended – Use the 10-noded Composite Tetrahedron instead
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1st Order Pentahedron (Wedge) Element 6-node elements with 1 Gauss integration points
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Use for transition elements in a HEX dominated mesh
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Useful in modeling axisymmetric structures
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LS-DYNA Keyword: *SECTION_SOLID
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ELFORM is always equal to 1 for mixed element types that include
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Element formulation options: ELFORM = 1
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Tetrahedrons
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Hexahedrons
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Pentahedrons
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Pyramids
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1st Order Pentahedron (Wedge) Element $ *ELEMENT_SOLID $ 1EID 2PID N1 N2 N3 N4 N5 N6 N7 N8 773 1 43 50 134 140 87 87 139 139 774 1 29 50 43 69 144 144 143 143 775 1 134 139 352 266 140 140 397 397 776 1 16 81 41 56 34 34 73 73 ……
$ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ SECTION DEFINITIONS $ $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $ *SECTION_SOLID $ 1SECID 2ELFORM 3AET 1 1 $
Penta elements are inside the HEX dominated mesh
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The Default Shell Element The default shell element is the fully integrated shell elements
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Fully integrated shell elements with assumed strain interpolants used to alleviate locking and enhanced in-plane bending behavior Local element coordinate system that rotates with the material to account for rigid body motion 4-node quadrilateral element or 3-node triangular element degenerated from 4-node quad element No need for hourglass control
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Belytschenko-Tsay Shell Element Belytschko-Tsay shell element formulation
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Shell element with reduced integration scheme Runs faster than the default shell element Co-rotational coordinate system Velocity-strain formulation instead of displacement-strain formulation
4-node quadrilateral elements or 3-node triangular elements degenerated from 4-node quad elements
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One point integration in the plane of the element
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Need hourglass control
LS-DYNA Keyword: *SECTION_SHELL
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Element formulation options: ELFORM = 2
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Belytschenko-Tsay Shell Element To change the shell element formulation • • •
Click on Analysis Settings Click on Solver Controls Change the Full Shell Integration from Yes to No
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Shell Elements: Misc Number of integration points through thickness
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To change the number of integration points
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Default is 3
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Define inside Section option for shells only
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Change the number in the Shell Sublayers
Warping can be controlled by using Belytschko-Wong-Chiang warping stiffness correction Can represent membrane elements with in-plane stress/strain only
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Hughes-Liu Beam Element Hughes-Liu beam element formulation, the default • • •
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Incrementally objective (rigid body rotations do not generate strains) Simple and run fast Include finite transverse shear strains No need for hourglass control Integration Scheme – One point along the axis – Multiple points in the cross-section, default is 2x2 Compatible with brick elements because it is based on a degenerated brick element formulation Reference surface can be offset – 0: midsurface – -1/+1: outer surfaces – Useful for modeling contact surfaces, connection of beam to solid elements, beam stiffeners in stiffened shells
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Cross-Sections of Beam Elements Beam Cross-Sections •
3 nodes are used to define the beam element
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The 3rd node is for the initial orientation of the beam element
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Beam Elements: Truss & cable To represent truss or cable elements •
Select the appropriate formulation in Section
LS-DYNA Keyword: *SECTION_BEAM •
Element formulation options: ELFORM = 3
