Coupling under trosional load, growing slipping regions (red)
with increasing load (by courtesy of Voith Turbo)

Static analyses with non-linear boundary conditions (contact problems) can be analyzed using the PERMAS-CA module.
Contact boundary conditions may be present between elastic bodies or between elastic bodies and a rigid counterpart. The bodies may behave also non-linearly.
There are several methods to describe contacts:

• by specification of the contact nodes in pairs,
• by specification of node sets for each contact zone (the node pairs are detected automatically),
• assignment of nodes / node sets to surfaces (incompatible meshes),
• general surface-to-surface contact (incompatible meshes).

The feature to define contact with incompatible meshes allows the independent meshing of the contacting bodies. This simplifies the modeling of complex contact surfaces (like tooth contact between gearwheels) essentially.
The direction of contact and the initial gap width may be specified explicitly or determined automatically from the geometry. Any press fit is easily modeled by the specification of a negative gap width.

Shaft-hub connection with friction, change of the
contact status (read: sliding, blue: sticking)

The contact analysis can include frictional contact using Coulomb friction (for slip and stick), which may be either isotropic or anisotropic.
The specification of a load history allows the correct simulation of any contact situation with slipping and sticking friction. This facilitates the convenient simulation of such situations in a quasi-static analysis.
The load history can be amended by pretensioning (e.g. of bolts), where the contact analysis is used to describe the pretension. In this way, the screw tightening torque is modeled by a known contact force in the barrel of the bolt.
Comprehensive checks allow the verification of contact models like type of contact, its geometry (gap width and normal vector), and the contact coordinate system (for normal and frictional force directions). In addition, the contact status is available for all iteration steps for checking purposes.
For frictional contact the quality of surfaces is of utmost importance. Therefore, PERMAS can smooth contact surfaces in order to improve frictional behavior essentially.
The analysis procedure uses a reduced flexibility model which is derived from the set of contact degrees of freedom. This procedure has the following advantages:

• The iteration is very efficient making it best suited for extremely large models with an arbitrary number of contact nodes.
• The accuracy of the results is fully preserved, because no additional stiffness is introduced by the modeling of contacts.

The simultaneous analysis of an arbitrary number of loading cases is possible. The contact parameters, i.e. gap width and coefficients of friction, may be different for each loading case. The contact boundary conditions are taken into account automatically by the static analysis procedure. No additional user request is required for a contact analysis.
In addition to all results usually derived from a static analysis the contact analysis provides for the contact status, the contact forces, the contact pressure, the gap widths, and the relative gap displacements.

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