ZeroLengthContactNTS2D

This command is used to construct a zeroLengthContactNTS2D element object. This is a Node-To-Segment (NTS) frictional contact element used in two dimensional analysis for contact between elements with 2 DOF nodes.

element zeroLengtContactNTS2Dh $eleTag -sNdNum $sNdNum -mNdNum $mNdNum -Nodes $Nodes $Kn $kt $phi

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$eleTag	unique element object tag
$sNdNum	Number of Slave Nodes
$mNdNum	Number of Master nodes
$Nodes ...	Slave and master node tags respectively
$Kn	Penalty in normal direction
$Kt	Penalty in tangential direction
$phi	Friction angle in degrees

NOTES:

1. The contact element is node-to-segment (NTS) contact. The relation follows Mohr-Coulomb frictional law: <math>T = N tan(\phi)</math>, where T is the tangential force, N is normal force across the interface and ,math>\phi</math> is friction angle.
2. For 2D contact, slave nodes and master nodes must be 2 DOF and notice that the slave and master nodes must be entered in counterclockwise order.
3. The resulting tangent from the contact element is non-symmetric. Switch to the non-symmetric matrix solver if convergence problem is experienced.
4. As opposed to node-to-node contact, predefined normal vector for node-to-segment (NTS) element is not required because contact normal will be calculated automatically at each step.
5. contact element is implemented to handle large deformations.

EXAMPLE:

element zeroLengthContactNTS2D 1 -sNdNum 6 -mNdNum 6 - Nodes 5 10 12 3 9 11 1 4 2 8 7 1e8 1e8 16

Example 1:

This example simply shows the two quadrilateral elements in normal contact. The top element is in normal downward uniform force. The Tcl script of this example can be found here <tcl>ZeroLengthContactNTS2D_Example1.tcl</tcl>.

Example 2:

This example shows two cantilever beams in contact. The beams were modeled using four-node quadrilateral elements and the end of top beam was subjected to a linearly increasing displacement. The Tcl scripts for this example can be found here.

The following Figure shows the deflections of the two beams.

REFERENCES:

1. P. Wriggers, V.T. Vu and E. Stein, Finite-element formulation of large deformation impact–contact problems with friction, Comput. Struct. 37 (1990), pp. 319–331.
2. Peter Wriggers. Computational Contact Mechanics. John Wiley & Sons Ltd. Chichester, 2002.

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Code Developed by: Roozbeh G. Mikola, UC Berkeley and N. Sitar, UC Berkeley