Flexural rigidity

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

Nonlinear Elasticity: From Single Chain to Networks and Gels

Abstract: Biological and polymeric networks show highly nonlinear stress–strain behavior manifested in materials that stiffen with increasing deformation. Using a combination of the theoretical analysis and molecular dynamics simulations, we develop a model of network deformation that describes nonlinear mechanical properties of networks and gels by relating their macroscopic strain-hardening behavior to molecular parameters of the network strands. The starting point of our approach is a nonlinear force/elongation relation for discrete chains with varying bending rigidity. The derived expression for the network free energy is a universal function of the first deformation invariant and chain elongation ratio that depends on a ratio of the unperturbed chain size to chain dimension in a fully extended conformation. The model predictions for the nonlinear shear modulus and differential shear modulus for uniaxial and shear deformations are in very good agreement with both the results of molecular dynamics simulations of...

Temperature-dependent bending rigidity of graphene

Abstract: Both previous theoretical and experimental work showed that the bending rigidity of a liquid membrane decreases with increasing temperature. We demonstrate that the elastic energy forms for a solid membrane and a liquid membrane are identical under equal-biaxial stretching, implying the bending rigidity of a solid membrane should decrease with increasing temperature. We perform molecular dynamics simulations to study how thermal fluctuation affects the bending rigidity of graphene, and find that the bending rigidity decreases exponentially with increasing temperature. This is in contrast with recent atomistic Monte Carlo simulation result that the bending rigidity of graphene increases with increasing temperature.

The Deformations and Stresses in Floating Ice Plates

Abstract: In the past, the analyses of floating ice plates subjected to static or dynamic loads were based on the theory of a thin homogeneous plate, although in actual floating ice plates Young's modulus may vary strongly with depth. Recently,A. Assur concluded, on the basis of a heuristic argument, that the solutions obtained for homogeneous plates may be used for floating ice plates, if a modified flexural rigidity is used. The purpose of the present paper is to study this question, by establishing a mathematically consistent formulation for the dynamic plate equation, utilizing Hamilton's Principle in conjunction with the three dimensional theory of elasticity. It is proven that for a variable Young's modulus and a constant Poisson's ratio the resulting formulations for plates and beams are the same as those for the corresponding homogeneous problems, if a modified flexural ridigity is used; thus confirmingAssur's conclusion. It is shown that the stress distribution is not linear and that the stress formula\(\sigma _{\max } = M{{z_0 } \mathord{\left/ {\vphantom {{z_0 } I}} \right. \kern- ulldelimiterspace} I}\) used by a number of investigators for the determination of the carrying capacity of a floating ice plate, as well as for the computation of failure stresses from tests on floating ice beams, is not applicable. Correct formulas are derived, corresponding stress distributions are presented and the consequences of the findings discussed.

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 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 the glass transition. This is accomplished by using embedded ultra-thin 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 two and four times greater than that at high temperature.