## Contact model definition

@CONTACT_MODEL_DEFINITION {
@CONTACT_MODEL_NAME {CntModlName} {
@INITIAL_CONTACT_FLAG {InitialContact}
@CHARACTERISTIC_PENETRATION_DISTANCE {εp}
@STIFFNESS_COEFFICIENT {kh}
@SPRING_NAME {SpringName}
@DAMPING_COEFFICIENT {μ}
@STRATEGY_PARAMETERS {qmin, α}
}
}
}

### NOTES

1. The contact model definition describes the parameters associated with the contact of two bodies of the model. This model is used in conjunction with the planar contact joint, the wheel element, and with the backlash model, for relative rotation or relative displacement elements. The forces generated at the point of contact can be divided into two parts: the normal forces and the tangential forces. The normal forces act in the direction normal to the plane tangent to the contacting bodies at the point of contact, whereas the tangential forces act in this plane. The parameters required for the computation of the normal contact forces are defined in this section, whereas the parameters associated with the evaluation of the tangential forces are described in the friction model.
2. If the bodies are in contact at the beginning of the simulation InitialContact = YES, otherwise InitialContact = NO.
3. ##### Figure 1. Penetration of contacting deformable bodies.
4. The contacting bodies are assumed to be deformable in a small region near the contact point. In this case, the center of mass of the bodies are allowed to approach each other closer than what would be allowed for rigid bodies. This quantity is defined as the approach and is denoted a; following the convention used in the literature, a > 0 when penetration occurs, as depicted in fig. 1. For the same situation, the relative distance q between the contacting bodies is negative. In a generic sense, the normal force of contact Fn can be separated into its elastic and dissipative components. A suitable expression for this force is Fn = Felas + Fdiss = dV/da + dV/da fd(da/dt) = dV/da [1 + fd(da/dt)], where V is the potential of the elastic forces of contact, and fd(da/dt) accounts for energy dissipation during contact.
5. The characteristic penetration distance, εp, is used to determine the proximity of the contacting bodies before contact occurs. Typically, εp is selected to be about 1% of the maximum approach a that will occur during the simulation. The elastic contact forces can be represented using either of the following two options
• If the @STIFFNESS_COEFFICIENT kh is defined, the relationship between the contact force and the penetration distance is assumed to be given by the solution of the Hertz contact problem, Fn = kh a3/2, where kh is the stiffness coefficient.
• If the @SPRING_NAME, SpringName, is defined, the elastic part of the contact force is assumed to be related to the approach through a nonlinear relationship that is represented by a nonlinear spring SpringName.
6. The dissipative force is represented by a linear damper as Fdiss = Felas μ da/dt, where μ is the linear damping coefficient.
7. When a contact model is used, it is necessary to switch on the time adaptivity feature for the time stepping procedure. When contact between the two bodies is about to take place, the contact model will dictate the time step for the analysis, as determined by the strategy parameters. Let q0 and q1 be the relative distance between the bodies for two consecutive time steps of size Δt0 and Δt1, respectively. To avoid large penetration distances and the ensuing large normal contact forces at the first time step after contact, the time step size will be selected so that the change in relative distance, Δq be of the order of the characteristic penetration distance. To achieve this goal, the desired change in relative distance is selected as Δq = εp if κ ≤ 1 and Δq = εp κα if κ > 1, where quantity κ, defined as κ = (q1p) / qmin, measures the proximity to contact. The desired time step size is the estimated as Δtnew = Δq / vm, where vm is the average relative velocity during the previous time step vm = 2 (q1 - q0) / Δt0 + Δt1. The default values of the strategy parameters are qmin = 5 and α = 1.2.
8. It is possible to attach comments to the definition of the object; these comments have no effect on its definition.

### Sensors

1. Sensors can be defined to extract information about contact models. The following SensorType and associated FrameName specifications are allowed for contact models: CONTACT_DATA, CONTACT_ETA_K, CONTACT_ETA_L. (Default value: DISPLACEMENTS).
2. No u value or v value are accepted for contact models.