Owing to their atomic thickness and low bending rigidity, suspended two-dimensional (2D) materials are prone to wrinkle formation. Here, we use molecular dynamics (MD) simulations to probe the effect of these wrinkles on the nonlinear elasticity of atomically thin graphene membranes. We observe a stress-strain response that consists of two linear regions that are separated by a transition. It is found that this transition is sharp in membranes where wrinkles are formed by uneven stresses at the boundaries. However, when wrinkles are formed by crystal defects, this nonlinear transition is seen to be more gradual. To capture these effects, we use a phenomenological model based on experimentally measurable quantities. We demonstrate the model's fidelity by fitting it to the MD simulated nonlinear response of many graphene membranes providing evidence that the sharpness of the transition between the linear regions in the stress-strain response is a measure of the type of wrinkles and can be quantified by our model.

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Despite numerous theoretical investigations on the mechanical properties of graphene, an accurate identification of its material behavior is still unattained. One hypothesis for this uncertainty is that modeling graphene as a static membrane cannot describe the strong coupling between mechanics and thermodynamics of this structure. Therefore, characterization methods built upon static models could not capture these effects. In this paper, we propose a new method for building a reduced order model for the dynamics of thermalized graphene membranes. We apply the proper orthogonal decomposition algorithm on time responses obtained from molecular dynamics simulations. As a result, a set of orthogonal modes is obtained which are then employed to build a reduced order model. The proposed model can describe the motion of the suspended graphene membrane over the whole spatial domain accurately. Moreover, due to its computational efficiency, it is more versatile for exploring the nonlinear dynamics of the system. This model is then employed for studying the nonlinear dynamics of graphene membranes at large amplitudes to extract Young's modulus. The obtained Young's modulus incorporates the effects of nano-scaled thermally induced dynamic ripples and hence, is temperature and size dependent. Our proposed atomistic modal order reduction method provides a framework for studying the dynamics and extracting the mechanical properties of other nano-structures at the molecular level.

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This paper investigates the complex bifurcation scenario of electrically-actuated circular micro-plates subjected to differential pressure. Our analysis deals with the primary, secondary and ultimate saddle-node bifurcation points responsible for the device snap-through and addresses the pressure range in which the robustness of the two main stable configurations is undermined by minor coexisting attractors. By making use of basins of attraction and integrity profiles, safe dynamical regions of motion are evaluated with respect to the applied DC voltage. It is found that period-doubling bifurcations are accountable for a sensible reduction in the dynamical integrity, small variations of the DC voltage largely modify the response of the pressure sensor.

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Despite theoretical predictions that graphene should be impermeable to all gases, practical experiments on sealed graphene nanodrums show small leak rates. Thus far, the exact mechanism for this permeation has remained unclear, because different potential leakage pathways have not been studied separately. Here, we demonstrate a sealing method that consists of depositing SiO₂ across the edge of suspended multilayer graphene flakes using electron beam-induced deposition. By sealing, leakage along the graphene-SiO₂ interface is blocked, which is observed to result in a reduction in permeation rate by a factor of 10⁴. The experiments thus demonstrate that gas flow along the graphene-SiO₂ interface tends to dominate the leak rate in unsealed graphene nanodrums. Moreover, the presented sealing method enables the study of intrinsic gas leakage through graphene membranes and can enable hermetic graphene membranes for pressure sensing applications.

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The bending rigidity of two-dimensional (2D) materials is a key parameter for understanding the mechanics of 2D NEMS devices. The apparent bending rigidity of graphene membranes at macroscopic scale differs from theoretical predictions at micro-scale. This difference is believed to originate from thermally induced dynamic ripples in these atomically thin membranes. In this paper, we perform modal analysis to estimate the effective bending rigidity of graphene membranes from the frequency spectrum of their Brownian motion. Our method is based on fitting the resonance frequencies obtained from the Brownian motion in molecular dynamics simulations, to those obtained from a continuum mechanics model, with bending rigidity and pretension as the fit parameters. In this way, the effective bending rigidity of the membrane and its temperature and size dependence, are extracted, while including the effects of dynamic ripples and thermal fluctuations. The proposed method provides a framework for estimating the macroscopic mechanical properties in other 2D nanostructures at finite temperatures.

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Electrostatic instability is one of the main features of many electrostatic MEMS and NEMS devices. In this paper, we investigate how the electrostatic instability of a plate-like electrode can be affected by a differential pressure. The results of this study indicate that the presence of differential pressure can have a significant influence on the equilibrium path, the number and location of unstable points, and the post-instability behavior. As a result, while the system is loaded and unloaded electrically, the electrostatic instability might lead to a snapping behavior. The noticed snapping behavior of a flat plate makes it very appealing for sensing and actuating applications. This study is based on both a semi-analytical framework and finite element simulations. The proposed analytical solution is shown to be accurate enough to be used as an effective tool for design.

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Surface stress-based measurement is a relatively new mechanism in biological and chemical sensing. The viability of this mechanism depends on the maximum sensitivity, accuracy, and precision that can be achieved with these sensors. In this paper, an analytical approximate solution and a finite-element model are employed to describe the electromechanical behavior of a surface stress-based sensor with capacitive measurements. In the proposed model, a circular membrane is assumed as the sensing component, while only a smaller concentric circular area of its surface is subjected to a change in surface stress. The presented approximate analytical solution has a good correspondence with the finite-element model and is computationally fast and accurate enough to be an effective design tool. Based on this modeling study, we can determine the optimum design of the sensor to obtain the maximum capacitive sensitivity. Moreover, we study the effect of this optimization on the precision of the system in surface stress sensing. This paper shows that the ratio of sensing area to the whole membrane plays a key role in the overall performance of such a sensor@en

Characterization of nonlinear behavior of micro-mechanical components in MEMS applications plays an important role in their design process. In this paper, nonlinear dynamics, stability and pull-in mechanisms of an electrically actuated circular micro-plate subjected to a differential pressure are studied. For this purpose, a reduced-order model based on an energy approach is formulated. It has been shown that nonlinear dynamics of an electrically actuated micro-plate, in the presence of differential pressure, significantly differs from those under purely electrostatic loads. The micro-plate may lose stability upon either saddle-node or period-doubling bifurcations. It has also been found that in the presence of a differential pressure, increasing the DC or AC voltages may surprisingly help to stabilize the motion of the micro-plate.

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In the last decades, Micro-Electro-Mechanical Systems (MEMS) have drawn immense attention due to their potential use in a wide variety of modern applications, including micro-mechanical sensors and actuators. MEMS are devices combining mechanical and electrical components between 1 and 100 micrometers, all integrated into a single chip. The performance of these devices hinges on the deflection and movement of these micro-mechanical components and clearly, improvement and innovation of MEMS require a comprehensive knowledge and in-depth understanding of the nonlinear mechanics of these components. In spite of the simple geometry of common micro-mechanical components, modeling the mechanics of micro-mechanical sensors and actuators is rather complex. In particular, the mechanics of micro-plates in electrostatic MEMS is entangled with two influential sources of nonlinearity namely, geometrical nonlinearity and the nonlinearity due to the presence of the electric field. These sources of nonlinearity are often the origin of instability and failure in MEMS devices, but might also be exploited to achieve, for example, higher sensitivity in the device. In either way, such nonlinearities shall be incorporated in the modeling and design of these micro-mechanical components. This thesis provides an investigation on nonlinear mechanics of micro-plates in electrostatic MEMS devices. Based on the proposed models, we are able to predict some phenomena in micro-plates that have not been noticed before and to study these aspects in a detailed level which was not possible previously. In particular, based on total potential energy and a Lagrangian approach, the nonlinear mechanics and stability of a clamped circular micro-plate in interaction with an electrostatic field is studied. The effects of different loading conditions (i.e. static and dynamic electric potential, and with or without the presence of a differential pressure) on the stability of such a system are addressed. The results of this study suggest that in presence of a differential pressure the steady-state motion of an electrically actuated micro-plate can be bi-stable or even multi-stable. In fact, a differential pressure can cause additional limit points and an unstable solution branch in the -static or dynamic- steady state solutions of the system. Saddle-node and period doubling bifurcations are repeatedly observed in the results and are recognized as main mechanisms of pull-in. Furthermore, one newly observed critical point in static loading is shown to be highly sensitive to the applied differential pressure suggesting the possibility of employing this limit point for sensing applications. In addition, this thesis provides a study on analyzing nano-plates within the framework of continuum mechanics. In this regard, the nonlinear vibrations of an electrically actuated graphene resonator is modeled and a methodology is proposed for characterization of its mechanical properties. In addition, the possibility of capturing the scaling effects in the mechanical behavior of nano-plates by employing a nonlocal continuum theory is addressed. As a result, two modification factors for the extensional and bending stiffness of nano-plates are presented to account for the effect of thickness in the nonlocal elasticity formulations. Finally, the mechanical performance and instability of a micro-plate as a transducer in surface stress sensing is investigated and an optimized design for such a sensor is proposed. It is shown that using the proposed optimized design, the sensitivity and overall reliability of such capacitive surface stress sensors can be significantly improved. The proposed techniques for modeling the mechanics of micro-plates in MEMS devices are simple and computationally efficient. They can provide in-depth insight into MEMS behavior and can be useful for designing MEMS with plate-like micromechanical components. @en

In the last decade, graphene membranes have drawn tremendous attention due to their potential application in Nano-Electro-Mechanical Systems. In this paper, we show that the frequency response curves of graphene resonators are powerful tools for their dynamic characterization and for extracting their equivalent Young's modulus. For this purpose, vibrations of an electrostatically actuated circular graphene membrane are studied both experimentally and numerically. The experiments reveal the dependency of the linear and nonlinear resonance frequency of the nano-resonator on the driving DC and AC voltages. A numerical model is proposed based on the nonlinear membrane theory, and by fitting the numerically calculated change in resonance frequency due to the DC voltage to those of the experimental observations, the Young's modulus is determined. It is shown that by using the obtained equivalent Young's modulus, the numerical model can accurately describe the nonlinear dynamics of the graphene membrane in other sets of measurements.@en

The electrostatic instability (pull-in) of a flat electrode in a parallel plate capacitor has been shown to be highly sensitive to external mechanical loads such as pressure. In this paper, we substantiate the possibility of prompting additional unstable configurations in such a system, with a remarkable sensitivity to the applied pressure. This additional instability has significant advantageous properties for sensing purposes. In addition to the high sensitivity and robustness of the pull-in voltage measurements, it can be adjusted so that after the unstable configuration is met, a snap-through to a new stable configuration occurs. As a result of this bi-stable behavior, the contact between the electrodes, which is the main drawback of pull-in phenomena, will be easily avoided. The results of this paper particularly suggest the suitability of this mechanism for two different methods of pressure measurements.

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