Fig. 4. Theory and FEA simulation of stress transmission on BP and NFPF surfaces.

(A) During sliding with lateral force F_LB, the BP exhibits extrusion stress at the front side and separates from the rear side. The corner of the pillar at the front side is denoted as corner A. h and d are the pillar height and diameter, respectively. P_Cap is the capillary stress generated by nano-liquid film and P(x) is the interfacial solid-solid contact stress along the x axis. (B) Finite element analysis (FEA) simulation of the contact stress P(x) on BP and a scaled-up soft BP pillar to demonstrate the structural deformation during friction. (C) Schematic diagram of the stress transmission on NFPF with stretching stress appearing at the front side. From rear to front, the fibers are marked from the first to Nth. (D) FEA simulation of the contact stress of NFPF and a scaled-up NFPF pillar to demonstrate the structural deformation during friction. (E) FEA simulation of the interfacial normal stress P_Inter of BP and NFPF array surfaces with a different number of pillars. (F) The process of multiple BP and NFPF separating from the substrate. Scale bars, 20 μm.