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### Contact

Contact is a strongly nonlinear kind of boundary condition, preventing bodies to penetrate each other. The contact definition implemented in CalculiX is based on a pairwise interaction of surfaces in the form of nonlinear springs.

Each pair of interacting surfaces consists of a dependent surface and an independent surface. The dependent surface must be defined based on nodes, the independent surface must consist of element faces (Figure 74). Usually, the mesh on the dependent side is finer than on the independent side. As many pairs can be defined as needed. A contact pair is defined by the keyword card *CONTACT PAIR.

Figure 74: Definition of the dependent nodal surface and the independent element face surface

For each node on the dependent surface, a face on the independent surface is localized such that a perpendicular line on a point within the face contains the node. If such is face is found a nonlinear spring element is generated consisting of the dependent node and all nodes belonging to the independent face. Depending of the kind of face the contact spring element contains 4, 5, 7 or 9 nodes. The properties of the spring are defined by a *SURFACE INTERACTION definition, whose name must be specified on the *CONTACT PAIR card.

The *SURFACE INTERACTION keyword card is very similar to the *MATERIAL card: it starts the definition of interaction properties in the same way a *MATERIAL card starts the definition of material properties. Whereas material properties are characterized by cards such as *DENSITY or *ELASTIC, interaction properties are denoted by the *SURFACE BEHAVIOR card. All cards beneath a *SURFACE INTERACTION card are interpreted as belonging to the surface interaction definition until a keyword card is encountered which is not a surface interaction description card. At that point, the surface interaction description is considered to be finished. Consequently, an interaction description is a closed block in the same way as a material description, Figure 3.

Right now, the *SURFACE BEHAVIOR card is the only surface interaction description card. It defines the exponential behavior of the spring element. The pressure exerted on the independent face of a contact spring element is given by

| (34)

Figure 75: Contact pressure

where is the pressure at zero clearance, is a coefficient and is the clearance. This is the distance from the dependent node to the independent face if the outward normal on the face points toward the dependent node, else it is minus the distance. Minus the clearance is also called the overclosure. Instead of having the specify , which lacks an immediate physical significance, the user is expected to specify which is the clearance at which the pressure is 1 % of . From this can be calculated:

| (35)

The pressure curve for and looks like in Figure 75. A large value of leads to soft contact, i.e. large penetrations can occur, hard contact is modeled by a small value of . Hard contact leads to slower convergence than soft contact.

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