Electro-mechanical Coupling in MEMS: Modeling and Experimental Validation

This paper presents the advantages of a strong coupled formulation to model the electro-mechanical coupling appearing in MEMS. The classical modeling approach is to use a staggered methodology iterating between two different programs to obtain the solution of the coupled problem. In this research a strong coupled formulation is proposed and a tangent stiffness matrix of the whole problem is computed. Using this matrix, nonlinear algorithms such as the Riks-Crisfield algorithm may be applied to solve the static nonlinear problem and accurately determine the static pull-in voltage. Moreover, the natural frequencies may be computed around each equilibrium positions. The dynamic behavior of the structure may also be studied and two new parameters are defined: the dynamic pull-in voltage and the dynamic pull-in time. This strong coupled methodology deriving from variational principle may also be used for topology optimization and extended finite elements

Model of Electrostatic Actuated Deformable Mirror Using Strongly Coupled Electro-Mechanical Finite Element

The aim of this paper is to deal with multi-physics simulation of micro-electro-mechanical systems (MEMS) based on an advanced numerical methodology. MEMS are very small devices in which electric as well as mechanical and fluid phenomena appear and interact. Because of their microscopic scale, strong coupling effects arise between the different physical fields, and some forces, which were negligible at macroscopic scale, have to be taken into account. In order to accurately design such micro-electro-mechanical systems, it is of primary importance to be able to handle the strong coupling between the electric and the mechanical fields. In this paper, the finite element method (FEM) is used to model the strong coupled electro-mechanical interactions and to perform static and transient analyses taking into account large mesh displacements. These analyses will be used to study the behaviour of electrostatically actuated micro-mirrors.Comment: Submitted on behalf of TIMA Editions (http://irevues.inist.fr/tima-editions

MAXIMIZATION OF PULL-IN VOLTAGE OF MICRO-ELECTROMECHANICAL STRUCTURES USING TOPOLOGY OPTIMIZATION

The design problem consists in maximizing the pull-in voltage using topology optimization method, which is formulated as an optimal material distribution. In addition to the classical volume constraint, different structural constraints could be taken into consideration. Sensitivity analysis is one of the key issues of the optimization process and is performed with the formulation of eigenvalue topology optimization problems. Here the paper investigates topology optimization of strongly coupled electromechanical systems. To avoid important modifications of the electric field by the optimization process, this first study considers a non design electrode and use topology optimization to design an optimal suspension structure. Solution procedure of the optimization problem is based on CONLIN optimizer using a sequential convex programming. This method that has proved its efficiency in many structural problems (sizing, shape) is here tailored to strongly coupled multiphysics design problems under consideration. The choice of appropriate explicit convex approximations schemes for multiphysic problems is investigated. The proposed method is illustrated and validated on microbeam optimization applications

Surveillance of cell wall diffusion barrier integrity modulates water and solute transport in plants

We acknowledge support from the ERA-NET Coordinating Action in Plant Sciences program project ERACAPS13.089_RootBarriers, with support from Biotechnology and Biological Sciences Research Council (grant no. BB/N023927/1 to D.E.S.), the German Research Foundation (DFG; grant no. FR 1721/2-1 to R.B.F. and the AgreenSkills+ fellowship programme to MC-P which has received funding from the EU’s Seventh Framework Programme under grant agreement N° FP7-609398 (AgreenSkills+ contract). This work was also funded by the Ministry of Education, Youth and Sports of the Czech Republic (National Program for Sustainability I, grant no. LO1204), the Swedish Governmental Agency for Innovation Systems (Vinnova) and the Swedish Research Council (VR). We thank Kevin Mackenzie (University of Aberdeen–Microscopy Histology Facility) and Carine Alcon (BPMP-PHIV microscopy platform) for assistance using the confocal microscope and stereo microscope for observing the root samples, and the Swedish Metabolomics Centre (http://www.swedishmetabolomicscentre.se/) for access to instrumentation.Peer reviewedPublisher PD

Advantages of an Energetic Approach to derive the Electro-Mechanical Coupling

This paper presents the advantages of a strong coupled formulation derived from the energy to model the electro-mechanical coupling appearing in MEMS. Usually classical softwares use a staggered methodology iterating between two different codes to obtain the solution of the coupled problem. Others use some additional links between the two fields to obtain a stronger coupling. In this research a strong coupled formulation derived from the total energy of the problem is proposed and has been presented by the author in paper.1 In this approach a new formulation of the electrostatic force is obtained and an analytical expression of the tangent stiffness matrix of the whole problem is derived. It has also been shown that this formulation of electrostatic forces provides a better convergence around corner.2 This paper will highlight the advantage to use this method in static, modal and dynamic simulation. Indeed using the tangent stiffness matrix, nonlinear algorithms such as the Riks-Crisfield algorithm may be applied to solve the static nonlinear problem and determine accurately the static pull-in voltage. Moreover, the natural frequencies may be easily computed around each equilibrium positions. The dynamic behaviour of the structure may also be studied and two characteristic parameters are computed: the dynamic pull-in voltage and the dynamic pull-in time. This strong coupled methodology deriving from variational principle may also be used for topology optimisation and extended finite elements

Introduction to Electromechanical Coupling

peer reviewedThis paper is dedicated to the physical understanding of electrostatic forces with a one-dimensional reference problem. First a non-dimensional analysis prescribes the kind of assumptions to consider for the electric field model. An analytical study of electro-mechanical coupling is then performed to understand the type of non-linearity added by electrostatic forces, and static and dynamic analysis are used to define new characteristic parameters. To come closer to more realistic problems, cubic mechanical stiffness is added to account for the large displacement hypothesis prescribed for certain types of MEMS and damping effects are studied

Finite Element Analysis of the Electro-Mechanical Coupling in MEMS

This paper concerns the modelling of the strong electro-mechanical coupling appearing in micro-electro-mechanical systems (MEMS). These systems are very small devices (typical size of a few microns), in which electric phenomena as well as mechanical and dynamical phenomena exist. The coupling between the electric and mechanical fields induce non-linear terms in the dynamic equilibrium equations of these microscopic structures so that instability may occur. In this paper, the finite element method (FEM) is used to perform modal analysis around non-linear equilibrium positions, taking into account large displacements

Modeling of Electro-Mechanical Coupling Problem using the Finite Element Formulation

A modeling procedure is proposed to handle strong electro-mechanical coupling appearing in micro-electromechanical systems (MEMS). The finite element method is used to discretize simultaneously the electrostatic and mechanical fields. The formulation is consistently derived from variational principles based on the electromechanical free energy. In classical weakly coupled formulations staggered iteration is used between the electrostatic and the mechanical domain. Therefore, in those approaches, linear stiffness is evaluated by finite differences and equilibrium is reached typically by relaxation techniques. The strong coupling formulation presented here allows to derive exact tangent matrices of the electro-mechanical system. Thus it allows to compute non-linear equilibrium positions using Newton-Raphson type of iterations combined with adaptive meshing in case of large displacements. Furthermore, the tangent matrix obtained in the method exposed in this paper greatly simplifies the computation of vibration modes and frequencies of the cou pled system around equilibrium configurations. The non-linear variation of frequencies with respect to voltage and stiffness can be then be investigated until pull-in appears. In order to illustrate the effectiveness of the proposed formulation numerical results are shown first for the reference problem of a simple flexible capacitor, then for the model of a micro-bridge