ABSTRACT
We present a new methodology to incorporate the Casimir forces within the molecular dynamics (MD) framework. At atomistic scales, the potential energy between two particles arising due to the Casimir effect can be represented as U(r ij ) = C/r 7. Incorporating the Casimir effect in MD simulations requires the knowledge of C, a problem hitherto unsolved. We overcome this by equating the total potential energy contributions due to each atomistic pair with the potential energy of continuum scale interacting bodies having similar geometries. After having identified the functional form of C, standard MD simulations are augmented with the potential energy contribution due to pairwise Casimir interactions. The developed framework is used to study effects of the Casimir force on the pull-in instability of rectangular and hollow cylindrical shaped deformable electrodes separated by a small distance from a fixed substrate electrode. Our MD results for pull-instability qualitatively agree with the previously reported analytical results but are quantitatively different. The effect of using longer-ranged Casimir forces in a constant temperature environment on the pull-in behaviour has also been studied.
ABSTRACT
Few advanced mechanics of materials solutions have found broader and more enduring applications than Emil Winkler's beam on elastic foundation analysis, first published in 1867. Now, 150 years after its introduction, this concept continues to enjoy widespread use in its original application field of civil engineering, and has also had a profound effect on the field of adhesion mechanics, including for soft matter adhesion phenomena. A review of the model is presented with a focus on applications to adhesion science, highlighting classical works that utilize the model as well as recent usages that extend its scope. The special case of the behavior of plates on incompressible (e.g., elastomeric and viscous liquid) foundations is reviewed because of the significant relevance to the behavior of soft matter interlayers between one or more flexible adherends.
ABSTRACT
We identify the temperature being measured by a thermometer in a nonequilibrium scenario by studying heat conduction in a three-dimensional Lennard-Jones (LJ) system whose two ends are kept at different temperatures. It is accomplished by modeling the thermometer particles also with the LJ potential but with added tethers to prevent their rigid body motion. These models of the system and the thermometer mimic a real scenario in which a mechanical thermometer is "inserted" into a system and kept there long enough for the temperature to reach a steady value. The system is divided into five strips, and for each strip the temperature is measured using an embedded thermometer. Unlike previous works, these thermometers are small enough not to alter the steady state of the nonequilibrium system. After showing initial transients, the thermometers eventually show steady-state conditions with the subregions of the system and provide values of the different temperature definitions-kinetic, configurational, dynamical, and higher-order configurational. It is found that their kinetic and the configurational temperatures are close to the system's kinetic temperature except in the two thermostatted regions. In the thermostatted regions, where the system's kinetic and the configurational temperatures are significantly different, the thermometers register a temperature substantially different from either of these two values. With a decrease in the system density and size, these differences between the kinetic and the configurational temperatures of the thermometer become more pronounced.
ABSTRACT
We study the influence of von Karman nonlinearity, van der Waals force, and a athermal stresses on pull-in instability and small vibrations of electrostatically actuated mi-croplates. We use the Galerkin method to develop a tractable reduced-order model for elec-trostatically actuated clamped rectangular microplates in the presence of van der Waals forcesand thermal stresses. More specifically, we reduce the governing two-dimensional nonlineartransient boundary-value problem to a single nonlinear ordinary differential equation. For thestatic problem, the pull-in voltage and the pull-in displacement are determined by solving apair of nonlinear algebraic equations. The fundamental vibration frequency corresponding toa deflected configuration of the microplate is determined by solving a linear algebraic equa-tion. The proposed reduced-order model allows for accurately estimating the combined effectsof van der Waals force and thermal stresses on the pull-in voltage and the pull-in deflectionprofile with an extremely limited computational effort.
ABSTRACT
A two-way coupled electromechanical theory is used to study static deformations and free vibrations of a laminated hybrid rectangular plate comprised of either piezoceramic (PZT) layers or patches embedded at arbitrary locations in graphite/epoxy layers. A first-order shear deformation theory is used to develop equations for the plate which are solved by the finite-element method (FEM) using eight-node isoparametric elements. Static deflections and natural frequencies computed with open-circuited PZT layers are found to differ significantly from those of grounded PZT layers.
