13.178. CONTA178 - 3D Node-to-Node Contact

Matrix or VectorGeometryShape Functions Integration Points
Stiffness MatrixNormal DirectionNoneNone
Sliding DirectionNoneNone
Load TypeDistribution
Element TemperatureNone - average used for material property evaluation
Nodal TemperatureNone - average used for material property evaluation

13.178.1. Introduction

CONTA178 represents contact and sliding between any two nodes of any types of elements. This node-to-node contact element can handle cases when the contact location is known beforehand.

CONTA178 is applicable to 3D geometries. It can also be used in 2D and axisymmetric models by constraining the UZ degrees of freedom. The element is capable of supporting compression in the contact normal direction and Coulomb friction in the tangential direction.

13.178.2. Contact Algorithms

Four different contact algorithms are implemented in this element.

  • Pure penalty method

  • Augmented Lagrange method

  • Pure Lagrange multiplier method

  • Lagrange multiplier on contact normal penalty on frictional direction

Pure Penalty Method

The Newton-Raphson load vector is:

(13–299)

where:

Fn = normal contact force
Fsy = tangential contact force in y direction
Fsz = tangential contact force in z direction

(13–300)

where:

Kn = contact normal stiffness (input FKN on R command)
un = contact gap size

(13–301)

where:

Ks = tangential contact stiffness (input as FKS on R command)
uy = contact slip distance in y direction
μ = coefficient of friction (input as MU on TB command with Lab = FRIC or MP command)

Augmented Lagrange Method

(13–302)

where:

ε = user-defined compatibility tolerance (input as TOLN on R command)

The Lagrange multiplier component of force λ is computed locally (for each element) and iteratively.

Pure Lagrange Multiplier Method

The contact forces (that is, Lagrange multiplier components of forces) become unknown DOFs for each element. The associated Newton-Raphson load vector is:

(13–303)

Lagrange Multiplier on Contact Normal Penalty on Frictional Direction

In this method only the contact normal face is treated as a Lagrange multiplier. The tangential forces are calculated based on penalty method:

(13–304)

13.178.3. Element Damper

The damping capability is only used for modal and transient analyses. Damping is only active in the contact normal direction when contact is closed. The damping force is computed as:

(13–305)

where:

V = relative velocity between two contact nodes in contact normal direction
Cv1 = constant damping coefficient (input as CV1 on R command)
Cv2 = linear damping coefficient (input as CV2 on R command)

13.178.4. Rigid Coulomb Friction

If you know that a CONTA178 element will be in sliding status throughout the analysis, and that the relative displacement of the two nodes will be monotonically increasing, the rigid Coulomb friction option (KEYOPT(10) = 7) can be used to avoid convergence problems. This option removes the stiffness in the sliding direction, as shown in Figure 13.32: Force-Deflection Relations for Rigid Coulomb Option. Note that if the relative displacement does not increase monotonically, the convergence characteristics of the rigid Coulomb friction law (KEYOPT(10) = 7) will be worse than for the elastic Coulomb friction law (KEYOPT(10) = 0).

Figure 13.32: Force-Deflection Relations for Rigid Coulomb Option

Force-Deflection Relations for Rigid Coulomb Option