Flexural rigidity

About: Flexural rigidity is a research topic. Over the lifetime, 3829 publications have been published within this topic receiving 56780 citations.

Elastic properties of surfactant monolayers at liquid–liquid interfaces: A molecular dynamics study

Abstract: Using a simple molecular model based on the Lennard–Jones potential, we systematically study the elastic properties of liquid–liquid interfaces containing surfactant molecules by means of extensive and large-scale molecular dynamics simulations. The main elastic constants of the interface, corresponding to the interfacial tension and the mean bending modulus are determined from the analyses of the long-wavelength behavior of the structure factor of the capillary waves. We found that the interfacial tension decreases with increasing surfactant interfacial coverage and/or surfactant chain length. However, we found that the corresponding change in the bending rigidity is nonmonotonic. Specifically, we found that the bending rigidity decreases with increasing surfactant interfacial coverage for small surfactant interface coverages, but then it increases as the surfactant interface coverage is further increased. Using a Gaussian theory on an interfacial Ginzburg–Landau model of surfactants, we find that the initial decrease of the bending rigidity is attributed to coupling between fluctuations of the surfactant orientation field to those in the interfacial height.

Simulation of mechanical parameters of graphene using the DREIDING force field

Abstract: Molecular mechanics/molecular dynamics (MM/MD) methods are widely used in computer simulations of deformation (including buckling, vibration, and fracture) of low-dimensional carbon nanostructures (single-layer graphene sheets (SLGSs), single-walled nanotubes, fullerenes, etc). In MM/MD simulations, the interactions between carbon atoms in these nanostructures are modeled using force fields (e.g., AIREBO, DREIDING, MM3/MM4). The objective of the present study is to fit the DREIDING force field parameters (see Mayo et al. J Phys Chem 94:8897–8909, 1990) to most closely reproduce the mechanical parameters of graphene (Young’s modulus, Poisson’s ratio, bending rigidity modulus, and intrinsic strength) known from experimental studies and quantum mechanics simulations since the standard set of the DREIDING force field parameters (see Mayo et al. 1990) leads to unsatisfactory values of the mechanical parameters of graphene. The values of these parameters are fitted using primitive unit cells of graphene acted upon by forces that reproduce the homogeneous deformation of this material in tension/compression, bending, and fracture. (Different sets of primitive unit cells are used for different types of deformation, taking into account the anisotropic properties of graphene in states close to failure.) The MM method is used to determine the dependence of the mechanical moduli of graphene (Young’s modulus, Poisson’s ratio, and bending rigidity modulus) on the scale factor. Computer simulation has shown that for large linear dimensions of SLGSs, the mechanical parameters of these sheets are close to those of graphene. In addition, computer simulation has shown that accounting for in-layer van der Waals forces has a small effect on the value of the mechanical moduli of graphene.

Beams with controllable flexural stiffness

Abstract: This paper describes a method to vary the flexural bending stiffness of a multi-layered beam. The multi-layered beam comprises of a base layer with polymer layers on the upper and lower surfaces, and stiff cover layers. Flexural stiffness variation is based on the concept that when the polymer layer is stiff, the cover layers are strongly coupled to the base beam and the entire multi-layered beam bends as an integral unit. In effect, we have a "thick" beam with contributions from all layers to the flexural bending stiffness. On the other hand, if the shear modulus of the polymer layers is reduced, the polymer layers shear as the base beam undergoes flexural bending, the cover layers are largely decoupled from the base, and the overall flexural bending stiffness correspondingly reduces. The shear modulus of the polymer layer is reduced by increasing its temperature through glass transition. This is accomplished by using embedded ultrathin electric heating blankets. From experiments conducted using two different polymer materials, polymer layer thicknesses and beam lengths the flexural stiffness of the multi-layered beam at low temperature was observed to be between 2-4 times greater than that at high temperature.

A strain-consistent elastic plate model with surface elasticity

Abstract: A strain-consistent elastic plate model is formulated in which both initial surface tension and the induced residual stress are treated as finite values, and the exactly same strain expressions are consistently employed for both the surface and the bulk plate. Different than most of previous related models which follow the original Gurtin–Murdoch model and include some non-strain displacement gradient terms (which cannot be expressed in terms of the surface infinitesimal strains or the von Karman-type strains) in the surface stress–strain relations, the present model does not include any non-strain displacement gradient terms in the surface stress–strain relations. For a free elastic plate with in-plane movable edges, the present model predicts that initial surface tension exactly cancels out the induced residual compressive stress. On the other hand, if all edges are in-plane immovable, residual stress cannot develop in the plate and the initial surface tension causes a tensile net membrane force. In addition, the present model predicts that initial surface tension reduces the effective bending rigidity of the plate, while this reduction does not depend on Poisson ratio. In particular, self-buckling of a free elastic plate under tensile surface tension cannot occur unless the effective bending rigidity of plate vanishes or becomes negative.

Dynamic Response of Plate on Elastic Half-Space

Abstract: Analytical results are presented for the dynamic response of a plate bearing on an elastic half-space and subjected to harmonic forces. The present work represents a departure from existing analyses in that herein both the flexibility and three-dimensionality of the plate are taken into account. Displacements and contact stresses are presented for square plates having a practical range of flexural stiffness. The harmonic analysis is conducted within the framework of a global stiffness solution, in which the plate and subgrade impedance matrices are formulated independently in accordance with a prescribed discretization pattern. Then compatibility of displacements and equilibrium of forces are enforced at the plate-subgrade interface. Solutions are presented for massless square plates subjected to harmonic point, uniform pressure, and moment loadings. The effect of the plate's mass on its response is studied by starting with a perfectly flexible massive plate and subsequently increasing the stiffness toward the limit of a completely rigid plate.