Geometric Effect on the Nonlinear Force-Displacement Relationship of Awl-Shaped Serpentine Microsprings for In-Plane Deformation

Even when made by brittle materials, awl-shaped serpentine microsprings (ASSMs) were found to have a nonlinear displacement–force relationship similar to springs made by ductile material. It is found that the nonlinear displacement–force relationship is due to the geometry and dimensions of the ASSMs. The geometric effect of the nonlinear force–displacement relationship of ASSMs for in-plane motion was investigated. A theoretical solution was derived to analyze this nonlinearity. By successfully fabricating and measuring an ASSM, the theoretical results agreed well with the experimental results. The results indicated that ASSMs have a nonlinear force–displacement relationship, which is similar to that of hardening springs. The taper angle has a significant effect on the nonlinear displacement of ASSMs. When the taper angle was small, no obvious effect appeared on the nonlinearity of the microsprings with different numbers of turns. When the beam length increased, the critical force for nonlinear deflection decreased.