Arnaud Lazarus

Effect of non-ideal clamping shape on the resonance frequencies of silicon nanocantilevers

In this paper, we investigate the effects of non-ideal clamping shapes on the dynamic behavior of silicon nanocantilevers. We fabricated silicon nanocantilevers using silicon on insulator (SOI) wafers by employing stepper ultraviolet (UV) lithography, which permits a resolution of under 100 nm. The nanocantilevers were driven by electrostatic force inside a scanning electron microscope (SEM). Both lateral and out-of-plane resonance frequencies were visually detected with the SEM. Next, we discuss overhanging of the cantilever support and curvature at the clamping point in the silicon nanocantilevers, which generally arises in the fabrication process. We found that the fundamental out-of-plane frequency of a realistically clamped cantilever is always lower than that for a perfectly clamped cantilever, and depends on the cantilever width and the geometry of the clamping point structure. Using simulation with the finite-elements method, we demonstrate that this discrepancy is attributed to the particular geometry of the clamping point (non-zero joining curvatures and a flexible overhanging) that is obtained in the fabrication process. The influence of the material orthotropy is also investigated and is shown to be negligible.

Contorting a heavy and naturally curved elastic rod

We investigate how the configurations obtained from the writhing of a heavy elastic rod are influenced by its intrinsic natural curvature. To this end, we perform a combination of numerics and precision model experiments on the compression or twisting of a thin rod. The ‘softness’ of these single elastic filaments stems from their slenderness (high aspect ratio), which allow for geometrically nonlinear compliant modes that can accommodate large deformations. We uncover the original mechanism that the presence of a body force (gravity in our case) delays the effect of natural curvature, which results from the complex interplay between geometrical constraints, elasticity and weight. We rationalize our experimental results by coupling the predictive power of a numerical method of our own, with classic theory for elastic rods under large deformations. This preponderance of geometry is relevant in systems over a wide range of length scales where curvature and body-forces often co-exist; from engineered rod-like structures such as wires, cables, and pipelines, to natural macromolecules, flagella, fibers and tendrils.

Buckling of an elastic ridge: competition between wrinkles and creases

We investigate the elastic buckling of a triangular prism made of a soft elastomer. A face of the prism is bonded to a stiff slab that imposes an average axial compression. We observe two possible buckling modes which are localized along the free ridge. For ridge angles ϕ below a critical value ϕ^{⋆}≈90°, experiments reveal an extended sinusoidal mode, while for ϕ above ϕ^{⋆}, we observe a series of creases progressively invading the lateral faces starting from the ridge. A numerical linear stability analysis is set up using the finite-element method and correctly predicts the sinusoidal mode for ϕ≤ϕ^{⋆}, as well as the associated critical strain ε_{c}(ϕ). The experimental transition at ϕ^{⋆} is found to occur when this critical strain ε_{c}(ϕ) attains the value ε_{c}(ϕ^{⋆})=0.44 corresponding to the threshold of the subcritical surface creasing instability. Previous analyses have focused on elastic crease patterns appearing on planar surfaces, where the role of scale invariance has been emphasized; our analysis of the elastic ridge provides a different perspective, and reveals that scale invariance is not a sufficient condition for localization.