depending on the type of non linear analysis you used, then conceptually the analysis takes the following steps (again depending on the type on analysis you use):
An iterative process starts:
A small increment of the load $\Delta F$ is applied (typically a percentage between 1% and 10%)
For those small load increments the displacements $\delta_i$ are ...
A "bonded contact" is presumably the same as welding the parts together.
Presumably, the material also has non-zero Poisson's ratio.
A friction coefficient of 0.01 will allow the ends of the pin to expand radially as it is compressed. The small but non-zero friction coefficient will stop the compressed pin from being perfectly cylindrical as it ...
Compute the wave velocity in a 3.05-m-diameter steel penstock having a
wall thickness of 25 mm if it:
i. is embedded in a concrete dam;
ii. is anchored at the upstream end; and
iii. has expansion joints throughout its length.