Temperature-dependent negative Poisson's ratio of monolayer graphene : prediction from molecular dynamics simulations

A temperature-dependent intrinsic property of monolayer graphene, the negative Poisson's ratio (NPR), is investigated in the present study. The classical molecular dynamics (MD) method is employed and the Erhart-Albe hybrid potential, i.e. the combination of the reactive empirical bond order (REBO) and the Tersoff potentials, is used for the graphene sheet in the numerical simulation. In the simulation process, the graphene sheet is assumed to be free standing with in-plane periodical boundary condition and under an ambient temperature up to 1000 K. Our study shows that the graphene NPR is decreased with the increase of temperature. Besides, we also perform the simulation of the graphene negative temperature expansion coefficient (NTEC) as an indirect validation of the present MD model. The characteristics of the nonlinear variations for both the NPR and the NTEC of a pristine graphene sheet are investigated. Our MD results at low temperature (0.1 K) further prove the intrinsic and anisotropic property of NPR for graphene

Large amplitude vibration of doubly curved FG-GRC laminated panels in thermal environments

A study on the large amplitude vibration of doubly curved graphene-reinforced composite (GRC) laminated panels is presented in this paper. A doubly curved panel is made of piece-wise GRC layers with functionally graded (FG) arrangement along the thickness direction of the panel. A GRC layer consists of polymer matrix reinforced by aligned graphene sheets. The material properties of the GRC layers are temperature dependent and can be estimated by the extended Halpin-Tsai micromechanical model. The modelling of the large amplitude vibration of the panels is based on the Reddy’s higher order shear deformation theory and the effects of the von Kármán geometric nonlinearity, the panel-foundation interaction and the temperature variation are included in the derivation of the motion equations of the panels. The solutions for the large amplitude vibration of the doubly curved FG-GRC laminated panels are obtained by applying a two-step perturbation approach. A parametric study is carried out to determine the influences of foundation stiffness, temperature variation, FG distribution pattern, in-plane boundary condition and panel curvature ratio on the natural frequencies and the nonlinear to linear frequency ratios of the doubly curved FG-GRC laminated panels

Effect of negative Poisson's ratio on the postbuckling behavior of pressure-loaded FG-GRMMC laminated cylindrical shells

Auxetic materials have emerged to be a new type of novel engineering materials with unique material properties. This paper reports the postbuckling behaviors of pressure loaded graphene-reinforced metal matrix composite (GRMMC) laminated cylindrical shells under the influence of in-plane negative Poisson's ratio (NPR) in temperature environments. The GRMMCs have temperature-dependent material properties which can be determined using an extended micromechanical model of Halpin–Tsai type. A cylindrical shell is made of GRMMC layers of different graphene volume fractions to achieve a piece-wise functionally graded (FG) pattern. The postbuckling equations for the pressure-loaded GRMMC laminated cylindrical shells are derived using the Reddy's third order shear deformation shell theory with the effects of von Kármán-type kinematic nonlinearity and temperature variation being included. Applying the singular perturbation technique in conjunction with a two-step perturbation approach, the governing equations for the shell postbuckling problem are solved. The results show that the postbuckling behaviors of pressure-loaded GRMMC laminated cylindrical shells are affected substantially by the in-plane NPR

Postbuckling behavior of functionally graded graphene-reinforced composite laminated cylindrical shells under axial compression in thermal environments

The current research deals with the postbuckling behavior of axially-loaded graphene-reinforced composite (GRC) laminated cylindrical shells under thermal environmental conditions. The piece-wise GRC layers are arranged in a functionally graded (FG) pattern along the thickness direction of the shells. The material properties of GRCs are assumed to be temperature-dependent and are estimated by the extended Halpin-Tsai micromechanical model. The governing equations for the GRC laminated cylindrical shells are based on the Reddy’s third order shear deformation shell theory and include the effects of the temperature variation. The nonlinearity effects are taken into account in the sense of von Kármán nonlinear kinematic assumptions. The buckling loads and the postbuckling equilibrium paths for the perfect and geometrically imperfect GRC laminated cylindrical shells can be obtained by solving the governing equations with a singular perturbation technique in conjunction with a two-step perturbation approach. The results show that the buckling loads and the postbuckling strengths of the GRC laminated cylindrical shells may be enhanced through piece-wise functionally graded distribution of graphene reinforcement

Thermomechanical postbuckling of unilaterally constrained shear deformable laminated plates with temperature-dependent properties

This paper presents a study on the postbuckling responses of shear deformable laminated plates resting on a tensionless foundation of the Pasternak-type and subjected to combined axial and thermal loads. Two different postbuckling cases are considered, namely (1) the compressive postbuckling of initially heated plates and (2) the thermal postbuckling of initially compressed plates. The postbuckling analysis of laminated plates is based on the higher order shear deformation plate theory with a von Kármán-type of kinematic non-linearity. It is assumed that the foundation reacts in compression only. The thermal effects are also included and the material properties are assumed to be temperature dependent. The initial geometric imperfection of the plates is taken into account. The analysis uses a two-step perturbation technique to determine the postbuckling response of the plates. An iterative scheme is developed to obtain numerical results without using any assumption on the shape of the contact region. Numerical solutions are presented in tabular and graphical forms to study the postbuckling behavior of antisymmetric angle-ply and symmetric cross-ply laminated plates resting on tensionless elastic foundations of the Pasternak-type, from which results for conventional elastic foundations are obtained as comparators. The results reveal that the unilateral constraint has a significant effect on the postbuckling response of the plates subjected to combined axial and thermal loads when the foundation stiffness is sufficiently large. The results also confirm that the postbuckling responses are significantly influenced by temperature dependency and initial membrane stress as well as initial thermal stress

Buckling and postbuckling of anisotropic laminated cylindrical shells under combined axial compression and torsion

A postbuckling analysis is presented for an anisotropic laminated cylindrical shell of finite length subjected to combined loading of axial compression and torsion. The governing equations are based on classical shell theory with von Kármán-Donnell-type of kinematic nonlinearity and including the extension-twist, extension-flexural and flexural-twist couplings. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine interactive buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, anisotropic laminated cylindrical shells for different values of load-proportional parameters. The results show that the postbuckling characteristics depend significantly upon the load-proportional parameter. The results reveal that in combined loading cases the postbuckling equilibrium path is unstable and the shell structure is imperfection-sensitive

Thermal buckling and postbuckling behavior of FG-GRC laminated cylindrical shells with temperature-dependent material properties

Thermal postbuckling analysis is presented for graphene-reinforced composite (GRC) laminated cylindrical shells under a uniform temperature field. The GRC layers are arranged in a functionally graded (FG) graphene reinforcement pattern by varying the graphene volume fraction in each GRC layer. The GRCs possess temperature dependent and anisotropic material properties and the extended Halpin–Tsai model is employed to evaluate the GRC material properties. The governing equations are based on a higher order shear deformation shell theory and include the von Karman-type kinematic nonlinearity and the thermal effects. A singular perturbation method in conjunction with a two-step perturbation approach is applied to determine the thermal postbuckling equilibrium path for a GRC shell with or without geometric imperfection. An iterative scheme is developed to obtain numerical thermal buckling temperatures and thermal postbuckling load–deflection curves for the shells. The results reveal that the FG-X piece-wise FG graphene distribution can enhance the thermal postbuckling capacity of the shells when the shells are subjected to a uniform temperature loading

Nonlinear response of nanotube-reinforced composite cylindrical panels subjected to combined loadings and resting on elastic foundations

This paper presents an investigation on the nonlinear behaviors of nanocomposite cylindrical panels subjected to the combined action of uniform lateral pressure and compressive edge loads. The panels may rest on elastic foundations and be in a varying temperature environment. The nanocomposite consists of reinforcing carbon nanotubes either uniformly distributed (UD) or functionally graded (FG) along the thickness direction of the panels. The two cases of nonlinear bending of initially compressed cylindrical panels and postbuckling of initially pressurized cylindrical panels are considered. A high-order shear deformation shell theory in association with von Kármán nonlinear strain-displacement relationships is applied to derive the governing equations for the carbon nanotube reinforced composite (CNTRC) panels. Furthermore, the effects of the panel-foundation interaction and the temperature variation are also included in the analysis and the material properties of CNTRC panels are assumed to be temperature-dependent. Numerical results are presented to illustrate the nonlinear bending responses and the postbuckling behaviors of CNTRC cylindrical panels resting on the Pasternak-type elastic foundations. The present solutions also highlight the effects of the CNT volume fraction, temperature rise, foundation stiffness as well as initial stress on the nonlinear behaviors of CNTRC cylindrical panels

Examination of thermal postbuckling behavior of temperature dependent FG-GRMMC laminated plates with in-plane negative Poisson's ratio

Auxetic composite laminates are a new type of engineering materials that have unique features for important potential applications. This paper examines the effect of in-plane negative Poisson's ratio (NPR) on the thermal postbuckling behaviors of graphene-reinforced metal matrix composite (GRMMC) plates. The plates rest on an elastic foundation and are subjected to a uniform temperature rise. The GRMMC layers with different volume fractions of graphene reinforcement can be arranged to achieve piece-wise functionally graded (FG) patterns across the plate thickness and the material properties of the GRMMC layers are temperature-dependent. The Reddy's third order shear deformation plate theory and the geometric nonlinearity of von Kármán-type are applied to formulate the thermal postbuckling equations for GRMMC laminated plates. The nonlinear problem can be solved by a two-step perturbation approach. Parametric study is performed for (±10)5T and (±10)3T GRMMC laminated plates possessing in-plane NPR. The results reveal that the buckling temperatures for (±10)5T and (±10)3T plates are significantly enhanced with an FG-X pattern for the plates. We found that due to the combined effect of FG and in-plane NPR, the thermal postbuckling strength of FG-X (±10)3T plate is higher than that of FG-X (±10)5T plate

Nonlinear bending of nanotube-reinforced composite cylindrical panels resting on elastic foundations in thermal environments

Nonlinear bending analysis is presented for nanocomposite cylindrical panels subjected to a transverse uniform or sinusoidal load resting on elastic foundations in thermal environments. Carbon nanotubes are used to reinforce the cylindrical panels in two distinguished patterns, namely, uniformly distributed (UD) and functionally graded (FG) reinforcements. The material properties of CNTRCs are assumed to be temperature-dependent and are estimated by a micromechanical model. The governing equations of the panel are derived based on a higher-order shear deformation theory with a von Kármán-type of kinematic nonlinearity and are solved by a two-step perturbation technique. The nonlinear bending behaviors of the CNTRC panels with different CNT volume fraction distributions, foundation stiffnesses, temperature rise, and the character of in-plane boundary conditions are studied in details