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Contact problems

If the formulation of some physical problem includes the nonpenetrability condition, we obtain the so called contact problem. Such problems often appear in simulations of engineering and civil engineering problems but also for example in medicine.

Different types of contact interface discretization

In most cases the contact condition is linearized in the normal direction of one chosen interface. In some cases, usually when we apriori know the solution, the bodies can be discretized in such way that after the deformation there will be matching nodes on the contact interface. The formulation of a contact condition in such cases is easy, but this concerns only special problems. Usually, the node to edge contact formulation when the contact conditions are satisfied in the nodes of one interface exactly. This formulation coming from engineering experience, however, brings several inconveniences such as jumps in contact stress. In recent years it is usual to use the mortar discretization which enforce the nonpenetration only in the integral form.

Types of contact problems

The basic problem is the contact of two bodies with mutual nonpenetrability or self nonpenetrability condition. This can be enhanced with the frictional condition in the tangential plane. The most common type of friction is according to Coulomb’s law. We can also compute with another physical quantity, for example with temperature, additional rules and laws should be taken into account, for example the generation of heat as the consequence of friction, heat conduction, etc.

Dynamical contact problems

When the usual time integration schemes are used for contact problems, the numerical instabilities appears quite often. We can illustrate it on the elastic impact of two billiard balls, when the part of kinetical energy transforms to deformation energy and back again . When the time integration scheme is not suited for contact problems, both bodies will vibrate so much that during the impact process, more than one collision will appear. Therefore, we use the stabilized Newmark’s scheme with the mass matrix redistribution.

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