A joining element has an anchoring portion for in-depth anchoring in the object and a head portion arranged proximally of the anchoring portion with respect to an insertion axis. The head portion has a lateral outer surface that has a structure that is well-defined, especially within tight tolerances. The joining element is positioned relative to an object of a non-liquefiable material such that the anchoring portion reaches into an opening of the object or is placed adjacent a mouth thereof. Then, the joining element is pressed towards a distal direction, to press the anchoring portion into the opening, while mechanical vibration energy is coupled into the joining element by a tool, in an amount and for a time sufficient for liquefaction of a portion of the thermoplastic material to cause interpenetration of the thermoplastic material into structures of the object.