# Unilateral contact

In mechanics, a unilateral contact denotes a mechanical constraint which prevents penetration between two bodies; see figure 1a. These bodies may be rigid or flexible. A unilateral contact is usually associated with a gap function g which measures the distance between the two bodies and a contact force. The behaviour of a unilateral contact is modeled by a force law which states a relation between the gap function and the contact force. Set-valued force laws of type Upr assume a hard contact and clearly distinguish between open contact (contact force equal to zero, gap g is positive) and closed contact (contact force is positive, gap g is zero), see figure 1b. Regularized force laws are associated to compliance models. These laws write the contact force as function of the gap, i.e. the models have the same underlying mathematical structure for closed and open contacts. Unilateral contacts are used in contact dynamics and/or contact mechanics.

Figure 1: a) unilateral contact, b) set-valued model, c) regularized model

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