Prediction of in-plane elastic properties of graphene in the framework of first strain gradient theory

Meccanica - In the present study, the in-plane elastic stiffness coefficients of graphene within the framework of first strain gradient theory are calculated on the basis of an accurate molecular...     

Inertia effects on the progressive crushing of aluminium honeycombs under impact loading

This paper presents the test results under quasi-static and impact loadings for a series of aluminum honeycombs (3003 and 5052 alloys) of different cell sizes, showing significantly different enhancements of the crushing pressure between 3003 honeycombs and the 5052 ones. A comprehensive numerical investigation with rate insensitive constitutive laws is also performed to model the experimental results for different cell size/wall thickness/base material, which suggests that honeycomb crushing pressure enhancement under impact loading is mostly due to a structural effect.Such simulated tests provide detailed local information such as stress and strain fields (in the cell wall) during the whole crushing process of honeycombs. A larger strain (in the cell wall) under impact loading than for the quasi-static case before each successive folding of honeycombs is observed, because of the lateral inertia effect. Thus, differences of the ratios of the stress increase due to strain hardening over the yield stress between 3003 and 5052 alloys lead to the different enhancements of crushing pressure. This result illustrates that the lateral inertia effect in the successive folding of honeycombs is the main factor responsible for the enhancement of the crushing pressure under impact loading.     

Natural modes and frequencies of in-plane vibrations of a fixed elastic ring

The natural modes and frequencies of an elastic ring fixed at a point are determined by numerically solving a boundary-value problem for a differential operator of the sixth order. The ring models a large circular antenna that slowly expands under zero gravity. The in-plane flexural vibrations of the ring are analyzed. Numerical results are presented     

Buckling and post-buckling of long pressurized elastic thin-walled tubes under in-plane bending

The present paper focuses on the structural stability of long uniformly pressurized thin elastic tubular shells subjected to in-plane bending. Using a special-purpose non-linear finite element technique, bifurcation on the pre-buckling ovalization equilibrium path is detected, and the post-buckling path is traced. Furthermore, the influence of pressure (internal and/or external) as well as the effects of radius-to-thickness ratio, initial curvature and initial ovality on the bifurcation moment, curvature and the corresponding wavelength, are examined. The local character of buckling in the circumferential direction is also demonstrated, especially for thin-walled tubes. This observation motivates the development of a simplified analytical formulation for tube bifurcation, which considers the presence of pressure, initial curvature and ovality, and results in closed-form expressions of very good accuracy, for tubes with relatively small initial curvature. Finally, aspects of tube bifurcation are illustrated using a simple mechanical model, which considers the ovalized pre-buckling state and the effects of pressure.     

Thermal buckling and postbuckling of FGM circular plates with in-plane elastic restraints

Based on von Karman's plate theory, the axisymmetric thermal buckling and post-buckling of the functionally graded material(FGM) circular plates with inplane elastic restraints under transversely non-uniform temperature rise are studied. The properties of the FGM media are varied through the thickness based on a simple power law. The governing equations are numerically solved by a shooting method. The results of the critical buckling temperature, post-buckling equilibrium paths, and configurations for the in-plane elastically restrained plates are presented. The effects of the in-plane elastic restraints, material property gradient, and temperature variation on the responses of thermal buckling and post-buckling are examined in detail.     

Simulation of non-selfadjoint control of thin elastic plates in the presence of conservative in-plane forces

Summary Based on the analysis presented in [1], a closed-form solution for the response of a controlled plate to a transversely applied dynamic loading is presented. Both the applied loading and the control are considered to be continuously distributed. The results and the corresponding parametric study are presented for two common boundary conditions of SSSS and SFSF in the plates. Received 11 March 1997; accepted for publication 18 March 1998     

Refined models of elastic beams undergoing large in-plane motions: Theory and experiment

Accurate mechanical models of elastic beams undergoing large in-plane motions are discussed theoretically and experimentally. Employing the geometrically exact theory of rods with appropriate kinematic assumptions and asymptotic arguments, two approximate models are obtained—a relaxed model and its constrained version—that describe extensional and bending motions and neglect shear deformations. These models are shown to be suitable to predict, via an asymptotic approach, closed-form nonlinear motions of beams with general boundary conditions and, in particular, with boundary conditions that longitudinally constrain the motions. On the other hand, for axially unrestrained or weakly restrained beams, an inextensible and unshearable model is presented that describes bending motions only. The perturbations about the reference configuration up to third order are consistently derived for all beam models. Closed-form solutions of the responses to primary-resonance excitations are obtained via an asymptotic treatment of the governing equations of motion for two different beam configurations; namely, hinged–hinged (axially restrained) and simply supported (axially unrestrained) beams. In particular, considering the present theory and the existing theories, variations of the frequency–response curves with the beam slenderness or the relative boundary mass are investigated for the lowest modes. The fidelity of the proposed nonlinear models is ascertained comparing the theoretically obtained frequency–response curves of the first mode with those experimentally obtained.     

Stability analysis of functionally graded rectangular plates under nonlinearly varying in-plane loading resting on elastic foundation

In this research work, an exact analytical solution for buckling of functionally graded rectangular plates subjected to non-uniformly distributed in-plane loading acting on two opposite simply supported edges is developed. It is assumed that the plate rests on two-parameter elastic foundation and its material properties vary through the thickness of the plate as a power function. The neutral surface position for such plate is determined, and the classical plate theory based on exact neutral surface position is employed to derive the governing stability equations. Considering Levy-type solution, the buckling equation reduces to an ordinary differential equation with variable coefficients. An exact analytical solution is obtained for this equation in the form of power series using the method of Frobenius. By considering sufficient terms in power series, the critical buckling load of functionally graded plate with different boundary conditions is determined. The accuracy of presented results is verified by appropriate convergence study, and the results are checked with those available in related literature. Furthermore, the effects of power of functionally graded material, aspect ratio, foundation stiffness coefficients and in-plane loading configuration together with different combinations of boundary conditions on the critical buckling load of functionally graded rectangular thin plate are studied.     

Bounds on the elastic and transport properties of two-component composites

Weshow in detail how the McCoy bounds on the effective shear modulus of a statistically isotropic composite, can be simplified and expressed in terms of the volume fraction, f₁, and two geometric parameters. ζ₁ and η₁. We simplify Silnutzer's bounds on the effective elastic moduli of fibre-reinforced composites and find they can be expressed in terms f₁and two geometric parameters, ζ'₁ and η'₁. The parameter ζ'₁ also determines bounds on the transport and optical constants of such composites. Also, the Elsayed-McCoy bounds on the transport properties of fibre-reinforced, symmetric-cell materials are shown to depend on three geometric parameters.     

On certain bounds for the in-plane translational stiffness of a disc inclusion at a bi-material elastic interface

This paper presents a set of bounds that can be used to estimate the in-plane translational stiffness of a rigid circular disc inclusion that is embedded at the interface between two dissimilar elastic half-space regions.     

The effect of cell irregularity on the high strain compression of 2D Voronoi honeycombs

The in-plane compression of low-density irregular Voronoi honeycombs with periodic boundary conditions has been simulated to engineering strains of 0.6 using finite element analysis. Different degrees of geometric irregularity in the honeycomb cells, as quantified using a regularity parameter, have been employed. The stress–strain predictions reveal that, for a fixed relative density, a more irregular honeycomb has a higher tangential modulus at low strain but supports a lower compressive stress at higher strain (above approximately 0.04) when compared with a more regular honeycomb. A combined ‘springs in parallel’ and ‘springs in series’ model has also been compared quantitatively with the simulation stress–strain results, the relative importance of the ‘springs in series’ mechanism having been found to increase with the irregularity of the honeycomb and, in many cases, with the applied compressive strain. In addition, the dependency of the Poisson’s ratio, the maximum bending strain in the cell walls, and the mean junction rotation upon the applied compressive strain have also been determined for a range of honeycomb irregularities.     

Seismic oscillations of an elastic rectangular structure protected by a viscoelastic stratum: in-plane problem

We study the problem of seismic protection of a rectangular elastic construction by mean of a viscoelastic stratum made of material of Kelvin–Voigt type. In particular we consider the in-plane problem. By using the standard boundary integral equations method (BIEs), the dynamic problem is reduced to a system of BIEs over the set of boundary lines. In order to reduce the dimension of the problem in its discrete form, for wave processes in the stratum and in the half-space foundation we use a special Green’s function satisfying the stress-free boundary conditions over the boundary of the half-space. A numerical algorithm is used to solve the problem after discretization and finally we discuss the physical meaning of the results and the efficiency of the seismic protection by the viscoelastic stratum.     

Anisotropy of elastic properties of materials

Papers dealing with the generalized Hooke’s law for linearly elastic anisotropic media are reviewed. The papers considered are based on Kelvin’s approach disclosing the structure of the generalized Hooke’s law, which is determined by six eigenmoduli of elasticity and six orthogonal eigenstates. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 131–151, November–December, 2008.     

Structure dependent elastic properties of supergraphene

Complete replacement of aromatic carbon bonds in graphene by carbyne chains gives rise to supergraphene whose mechanical properties are expected to depend on its structure. However, this dependence is to date unclear. In this paper, explicit expressions for the in-plane stiffness and Poisson’s ratio of supergraphene are obtained using a mole-cular mechanics model. The theoretical results show that the in-plane stiffness of supergraphene is drastically (at least one order) smaller than that of graphene, whereas its Pois-son’s ratio is higher than 0.5. As the index number increases (i.e., the length of carbyne chains increases and the bond density decreases), the in-plane stiffness of supergraphene decreases while the Poisson’s ratio increases. By analyzing the relation among the layer modulus, in-plane stiffness and Poisson’s ratio, it is revealed that the mechanism of the faster decrease in the in-plane stiffness than the bond density is due to the increase of Poisson’s ratio. These findings are useful for future applications of supergraphene in nanomechanical systems.