# Bi-Stability in Flexure Beams: Introducing a Setup for Experimental Characterization
## 3 Results and Discussion
### Flexure Beams Deformation  
Besides the study of the hard data obtained by the texture analyzer, there is relevance in investigating the form of the flexure beams to validate the behavior observed in previous sections. The snapping sequence presented in Figure 1b shows that the system has three main buckling shapes as it moves along the slider. This section explores the deformation of the flexure beams at those points: the beginning, end, and snap-through moment, according to their thickness. The deformation of the flexure beams was analyzed by observing the specimens throughout the tests and through a thoughtful examination of the pictures and videos taken during the experiments. Before being placed in the setup, the form of the flexure beams is completely straight, without deformations. Once allocated in the fixture, the 55 mm long flexure is compressed to fit a 50 mm width, acquiring the shape of an arch. As expected, under axial compression, the beam buckles to its initial form, which is the first state equilibrium position. The arch doesn't reach its maximum height because it is restrained by the length of the slider. Therefore, the initial arches are slightly prestressed. This can be noticed in the starting point of the force-distance graphs in Figure 5, where the curves do not start at zero Newtons of force. Figure 9: (**a–d**) Snap-through points in relation to the load cycle graphs. The straightness of the curves suggests that the mechanisms travel a similar linear distance before snapping-through, regardless of the load number. At the snap-through point, the system arrives at its unstable equilibrium position. Although buckling modes are difficult to predict, we observe that, at the _STP_, the arches of all sample beams remain symmetric about their centers, which means that both sides of the arch buckle in the same direction (upwards or downwards). In contrast, other studies found in the literature show both symmetrical and asymmetrical buckling modes [28; 32; 33]. Differences could be attributed to various sources. First, those samples in [28; 32; 33] consisted of a single beam, while those tested here are two independent beams loaded at the center. Regardless of the symmetry of the arches, the buckling direction in samples c20 and c30 varies. Figure 10c,d show these variations at the samples that buckle upwards or downwards indistinctively. Furthermore, Figure 10a,b,e show all c10, c15, and c40 samples buckled upwards. Figure 10: Image of samples used for the “Performance by thickness” experiments, at their snap-through points. (**a**) Samples of c10 flexure beams (0.25 mm) (**b**) Samples of c15 flexure beams (0.38 mm) (**c**) Samples of c20 flexure beams (0.50 mm) (**d**) Samples of c30 flexure beams (0.50 mm) (**e**) Samples of c40 flexure beams (1.00 mm). As the beams are homogeneous and isotropic, there is no preference for buckling up or down. The diversity of buckling directions also seems irrelevant to the force-distance behavior of the beams. However, the change in thickness of the flexure beams affects the buckling beam's non-linearity, thus the mechanical behavior. As observed in Figure 10a-c, thinner beams present smooth arches during snapping, but the curvature becomes less smooth as they increase thickness. c30 and c40 arches tend to bend toward the central slider, adding stress to the joints. Samples c30-1 and c40-1 even bend sharply near the joint, causing a partial fracture. This condition is exposed in Figure 8d,e. Nevertheless, the thickness of the flexure beams impacts their deformation considerably. Figure 1b shows the form of a typical arch in its first stable equilibrium position which appears symmetrical and presents a smooth curvature. The thinner flexure beams c10, c15, and c20 seem to have such forms. In contrast, the arches of large calibers (c30 and c40) tend to be irregular and harder to set up. Although all samples are completely straight before being placed in the setup, most of them deform permanently after being compressed.