Contact stiffness of the multi-indenter contact interface

Mechanical contact plays a pivotal role in both industrial and daily life applications. Contact stiffness of a multi-indenter contact interface fundamentally determines force–deformation relations. However, the understanding of the overall contact stiffness from the historical perspective is limited owing to inherent difficulties in precisely characterizing the interaction in multi-indenter contacts. In this study, the mechanical strong interaction among indenters is pinpointed. A theoretical model for accurately determining the contact stiffness of multi-indenter contact interface is developed. The physical mechanism of the contact stiffness of multi-indenter contact interface is revealed. The theoretical model is solidly validated by experiment and simulation. More importantly, the present theoretical model can predict the contact stiffness of contact interfaces with complex and irregular configurations, which may be filled up with indenters of hierarchical structures. The critical load is determined to guarantee the finished product rate during transfer printing. This is experimentally evidenced by the transfer printing of silicon wafer with complexly customized patterns. The present study provides a profound guidance for various engineering applications such as fabrication and integration of micro- and nano-electronic chips as well as electronic devices.