The shifted penalty method

The method presented here is a variation of the classical penalty one, suited to reduce penetration of the con- tacting surfaces. The slight but crucial modification concerns the introduction of a shift parameter that moves the min- imum point of the constrained potential toward the exact value, without any penalty increase. With respect to the clas- sical augmentation procedures, the solution improvement is embedded within the original penalty contribution. The problem is almost consistently linearized, and the shift is updated before each Newton’s iteration. However, adding few iterations, with respect to the original penalty method, a reduction of the penetration of several orders of magni- tude can be achieved. The numerical tests have shown very attractive characteristics and very stable solution paths. This permits to foresee a wide area of applications, not only in con- tact mechanics, but for any problem, like e.g. incompressible materials, where a penalty contribution is required.