Nonlinear Penalty Curve (Nonlinear Analysis)

In the previous section, Linear Penalty Curve was discussed, wherein, the contact stiffness remains constant when either in the open or closed configuration, and only changes when the contact status is updated.

This may, in some small number of cases, lead to convergence difficulties due to the sudden and highly discontinuous nature of the stiffness change. To help smooth the stiffness change at the contact open/close location, nonlinear penalty curves can be used via the STFEXP and STFQDR continuation lines on the PCONT entry. Nonlinear penalty curves are currently applicable to N2S and S2S contact discretizations.

Exponential Nonlinear Penalty

For S2S contact, the force Fx in Figure 1 denotes contact pressure.


Figure 1. Exponential Nonlinear Penalty Curve Has Three Regions

C0 and P0 are specified on the corresponding fields in the STFEXP continuation line. Kfinal and C1 are automatically determined by the C0, P0, and the STIFF fields.

Quadratic Nonlinear Penalty

For S2S contact, the force Fx in Figure 2 denotes contact pressure.


Figure 2. Quadratic Nonlinear Penalty Curve Has Four Regions
C0, ALPHA1, ALPHA2, and ALPHA3 are specified on the corresponding fields in the STFQDR continuation line. Kfinal is automatically determined based on the STIFF field. C1, C2, and Kinitial are defined as:
  • ALPHA1 = C1/ (Characteristic Length)
  • ALPHA2 = (C2 + C0)/(C1 + C0)
  • ALPA3 = Kinitial/Kfinal

The exponential and quadratic nonlinear penalty definitions are currently not applicable to FREEZE contact. They are also ignored for contacts in linear analysis.