Numerical multiscale modelling of nonlinear elastowetting

International audienceWe investigate here the static finite deformation of two (or more) three-dimensional nonlinear elastic solids which merged in a third medium, define a triple line (TL). The total energy, accounting for elastic, surface and possible gravity potentials is then minimized numerically in order to solve two physical problems of interest: (i) a soft incompressible axisymmetric drop at rest on a stiffer substrate and (ii) a stiff drop at rest upon a softer substrate, both in situations of strong substrate surface tension effects. Because of the interplay between surface and bulks properties, the behavior of the TL is related to another smaller length-scale (typically micrometer scale) than the elastic solids length-scale (typically millimeter scale). A unified deformability parameter relating all scales is introduced and a multi-scale discretization of the domain is used. A first example approached by our model is the elasto-wetting problem in which a very soft drop sits on a stiffer elastic solid. The numerical predictions of our model are compared with the analytical results of the linear elastic theory. In particular, our computations show that the Laplace pressure, together with the asymmetry of the solid surface tensions (between the wet and dry part of the interface), account for the rotation of the cusp of the ridge. In the second example, motivated by indentation problems of a nonlinear elastic substrate by a stiff sphere, we analyse the interplay of the solid surface tensions and elasticity at a small-scale. The numerical results also show that gravity might have an important effect and must be included in any micro-scale modelling

Evolution of regular bent rectangles by the driven crystalline curvature flow in the plane with a non-uniform forcing term

We study the motion of regular bent rectangles driven by singular curvature flow with a driving term. The curvature is being interpreted as a solution to a minimization problem. The evolution equation becomes in a local coordinate a system of Hamilton-Jacobi equations with free boundaries, coupled to a system of ODE’s with nonlocal nonlinearities. We establish local-in-time existence of variational solutions to the flow and uniqueness is proved under additional regularity assumptions on the data

Casimir Effect on Amplitude-Frequency Response of Parametric Resonance of Electrostatically Actuated NEMS Cantilever Resonators

This paper deals with the effect of Casimir force on the amplitudefrequency response of parametric resonance of electrostatically actuated nanoresonators. The resonator is actuated by using an electrostatic force to include a f irst order fringe correction. Casimir force and viscous damping force are included in the model, as well. Both electrostatic and Casimir forces are nonlinear. The behavior of the resonator is investigated using two methods, the Method of Multiple Scales (MMS) for a Reduced Order Model (ROM) using one mode of vibration, and numerical integration of ROMs using up to five modes of vibration. ROM is based on the application of a Galerkin procedure that uses the undamped mode shapes of the cantilevered beam as the basis of functions. The amplitude-frequency response consists of two bifurcations, namely subcritical and supercritical. The increase of Casimir effect shows an increase of the interval of frequencies of the unstable zero steady-state solutions, and a larger range of frequencies for which the system has stable steady-state solutions for amplitudes larger than 0.5 of the gap

Integrated source and channel encoded digital communication system design study

The analysis of the forward link signal structure for the shuttle orbiter Ku-band communication system was carried out, based on the assumptions of a 3.03 Mcps PN code. It is shown that acquisition requirements for the forward link can be met at the acquisition threshold C/N0 sub 0 value of about 60 dB-Hz, which corresponds to a bit error rate (BER) of about 0.001. It is also shown that the tracking threshold for the forward link is at about 57 dB-Hz. The analysis of the bent pipe concept for the orbiter was carried out, along with the comparative analysis of the empirical data. The complexity of the analytical approach warrants further investigation to reconcile the empirical and theoretical results. Techniques for incorporating a text and graphics capability into the forward link data stream are considered and a baseline configuration is described