In transient dynamic analysis with contact, if the contact and target surfaces impact each other with nonzero relative velocities, it is important to satisfy momentum and energy balance for the contact/target interface. This helps to more accurately predict the duration of impact and the rebound velocities after separation. This can be achieved by using impact constraints with any of the 2D or 3D contact elements: CONTA172, CONTA174, CONTA175, CONTA177, and CONTA178.
Impact constraints include constraints on penetration and relative velocity (see Energy and Momentum Conserving Contact in the Theory Reference). To activate the impact constraints the following contact options must be defined for a contact element:
Contact algorithm must be one of the following:
Augmented Lagrangian (KEYOPT(2) = 0)
Penalty function (KEYOPT(2) = 1)
Lagrange multiplier on contact normal and penalty on tangent (KEYOPT(2) = 3)
Pure Lagrange multiplier on contact normal and tangent (KEYOPT(2) = 4)
Standard or rough contact (KEYOPT(12) = 0 or 1)
Impact constraints (KEYOPT(7) = 4)
The impact constraints can be used with both frictionless and frictional contact.
The impact constraints are active only on the contact/target interface, so energy conservation is enforced only for contact elements. The underlying finite elements defining the interior of impacting bodies do not satisfy energy conservation. To ensure energy conservation, the following conditions must be satisfied for contact elements:
Relative velocity constraint should be satisfied exactly.
No numerical damping should be used.
No friction should be specified.
Energy conservation is relatively easy to satisfy for rigid impact (when both contact and target surfaces are rigid) as compared to flexible impact (when the target surface is rigid and the contact surface is flexible, or both surfaces are flexible). This is because the underlying finite elements for flexible bodies excite higher frequencies, which can make the time integration scheme unstable unless some numerical damping is used. For rigid bodies undergoing only translation motion and impact, numerical damping is generally not needed. However, when rigid bodies are undergoing large rotations, a small amount of numerical damping is necessary to keep the time integration scheme from becoming unstable.
An automatic time-stepping scheme adjusts the time-increment size. It starts adjusting the size of the time increments before impact such that there is minimum penetration in the substep where contact is first detected. This is important because the contact algorithm enforces the relative velocity constraints only to prevent further penetration.
If the automatic time stepping scheme is not used (AUTOTS,OFF), there may be some uncontrolled penetration of the surfaces depending on the size of the time increment for the substep where contact is first detected before the relative velocity constraint prevents further penetration.
When using fixed time increment, fixed number of substeps, or automatic time stepping (AUTOTS,ON), you should make sure that the penetrations remain sufficiently small.
When using the impact constraints, the penetration value depends on two factors:
Size of the time increment where contact is first detected
Accuracy of relative velocity constraint
The "initial" penetration value depends on the size of the time increment, as explained above. There is no contact force associated with this value. The remaining penetration value comes from the enforcement of relative velocity constraint using the contact algorithm. The value of this penetration depends on the choice of contact algorithm, contact normal stiffness (FKN), and/or allowable penetration (FTOLN). The contact normal force is directly related to this penetration value.
When using impact constraints to model impact between rigid bodies, a coefficient of restitution (real constant COR) can be used to model loss of energy during impact. The coefficient of restitution defines the ratio of relative velocity of rigid bodies after impact to relative velocity of rigid bodies before impact, so its value varies between 0 and 1. A value of 0 indicates that the rigid bodies stick to each other after impact, while a value of 1 indicates that the rigid bodies rebound after impact with the magnitude of relative velocity after impact being the same as before impact. COR defaults to 1.
To model a perfect plastic impact (COR = 0), you should enter a small number (for example, 1x10-6) instead of 0, as entering COR = 0 will make use of the default (COR = 1).
The use of COR is recommended only for rigid-rigid contact. For contact between deformable bodies, the deformation mechanisms of the bodies will result in energy loss—an affect that COR tries to capture.