Buckling and postbuckling of biaxially compressed functionally graded multilayer graphene nanoplatelet-reinforced polymer composite plates

The present paper investigates the biaxially compressed buckling and postbuckling behaviors of functionally graded multilayer composite plates reinforced with a low content of graphene nanoplatelets (GPLs) that are randomly oriented and uniformly dispersed in the polymer matrix within each individual layer. The material properties of the GPL-reinforced composite (GPLRC), which are graded along the thickness direction due to a layer-wise change in GPL weight fraction, are evaluated through a micromechanics model. Theoretical formulations are based on the first-order shear deformation plate theory and von Karman-type nonlinear kinematics and include the effect of an initial geometric imperfection. A two step perturbation technique is employed to determine the asymptotic postbuckling solutions and the biaxial compressive postbuckling equilibrium paths of both perfect and imperfect plates simply supported on all edges. The effects of GPL weight fraction, distribution pattern, geometry and size as well as total number of layers on the buckling and postbuckling behaviors of functionally graded GPLRC plates are examined in detail. (C) 2017 Elsevier Ltd. All rights reserved

Extension of Barlat’s Yield Criterion to Tension–Compression Asymmetry: Modeling and Verification

The present study is devoted to extending Barlat’s famous yield criteria to tension–compression asymmetry by a novel method originally introduced by Khan, which can decouple the anisotropy and tension–compression asymmetry characteristics. First, Barlat (1987) isotropic yield criterion, which leads to a good approximation of yield loci calculated by the Taylor–Bishop–Hill crystal plasticity model, is extended to include yielding asymmetry. Furthermore, the famous Barlat (1989) anisotropic yield criterion, which can well describe the plastic behavior of face-centered cubic (FCC) metals, is extended to take the different strength effects into account. The proposed anisotropic yield criterion has a simple mathematical form and has only five parameters when used in planar stress states. Compared with existing theories, the new yield criterion has much fewer parameters, which makes it very convenient for practical applications. Furthermore, all coefficients of the criterion can be determined by explicit expressions. The effectiveness and flexibility of the new yield criterion have been verified by applying to different materials. Results show that the proposed theory can describe the plastic anisotropy and yielding asymmetry of metals well and the transformation onset of the shape memory alloy, showing excellent predictive ability and flexibility

Primary and secondary resonances of functionally graded graphene platelet-reinforced nanocomposite beams

The present study investigated the nonlinear harmonic vibration of functionally graded multilayer graphene nanoplatelet (GPL)-reinforced nanocomposite beams on the basis of the third-order shear deformation theory. The GPL volume fraction shows a layer-wise change, while in each individual layer GPLs are uniformly dispersed in the matrix. The effective Young’s moduli of the GPL-reinforced nanocomposite (GPLRC) beams were estimated through the Halpin–Tsai micromechanics model. The mass densities as well as the effective Poisson’s ratios of the GPLRC beams were predicted by the rule of mixture. The nonlinear partial differential equations of motion were discretized by means of the Galerkin procedure. A parametric study was carried out by using the multiple scales method to examine the effects of GPL distribution pattern, weight fraction, geometry, and size on the nonlinear response of the primary, secondary, and combination resonances. Results show that an addition of a very low weight fraction of GPL nanofillers significantly reduces the primary, superharmonic, subharmonic, and combinational resonant responses of the beams. The square-shaped GPLs with fewer graphene layers are the most favorable reinforcements

Thermal buckling and postbuckling of edge-cracked functionally graded multilayer graphene nanocomposite beams on an elastic foundation

This paper investigates thermal buckling and postbuckling behaviors of functionally graded graphene nanoplatelet (GPL)-reinforced composite multilayer beams containing an open edge crack and resting on a Pasternak-type elastic foundation based on the first-order shear deformation beam theory including von Kármán geometric nonlinearity. The material properties of functionally graded GPL-reinforced composites (GPLRCs), which exhibit piece-wise variation along the thickness direction, are evaluated using micromechanics based models. The bending stiffness of the cracked section is estimated by the rotational spring model. The obtained nonlinear partial differential equations of equilibrium are discretized by the differential quadrature method, and then an iterative method is used to obtain the thermal buckling loads and postbuckling load-deflection curves. Detailed parametric studies are conducted to investigate the effects of crack length, GPL distribution pattern, GPL weight fraction, GPL length-to-width and length-to-thickness ratios, boundary conditions, and foundation stiffnesses on the thermal buckling loads and postbuckling response of the cracked GPLRC beams

Nonlinear free vibration of cracked functionally graded graphene platelet-reinforced nanocomposite beams in thermal environments

The present paper studies the nonlinear free vibration of edge-cracked graphene nanoplatelet (GPL)-reinforced composite laminated beams resting on a two-parameter elastic foundation in thermal environments. GPL nanofillers are assumed to be randomly oriented and are functionally graded distributed in a layer-wise pattern along the beam thickness. The temperature field considered is assumed to be a uniformly distributed in the domain of the beam. Effective material properties of the GPL-reinforced nanocomposite (GPLRC) are estimated by micromechanical models. Stress intensity factors are calculated based on the finite element methods. In the framework of the first order shear deformation beam theory, the equations of motion of cracked GPLRC beams are established including the von Kármán-type geometric nonlinearity. The bending stiffness of the cracked section is evaluated by the massless rotational spring model. The differential quadrature method is used to calculate the linear and nonlinear natural frequencies of the cracked beams. Numerical results illustrate the effects of GPL distribution pattern and concentration, GPL geometry and size, crack length, foundation stiffnesses and temperature variation on the linear and nonlinear free vibration characteristics of the cracked GPLRC beams

Low-velocity impact response of geometrically nonlinear functionally graded graphene platelet-reinforced nanocomposite plates

This paper investigates the low-velocity impact response of functionally graded multilayer nanocomposite plates reinforced with a low content of graphene nanoplatelets (GPLs) in which GPLs are randomly oriented and uniformly dispersed in the polymer matrix within each individual layer with GPL weight fraction following a layer-wise variation along the plate thickness. The micromechanics-based Halpin–Tsai model is used to evaluate the effective material properties of the GPL-reinforced composite (GPLRC), and the modified nonlinear Hertz contact theory is utilized to define the contact force between the spherical impactor and the GPLRC target plate. The equations of motion of the plate are derived within the framework of the first-order shear deformation plate theory and von Kármán-type nonlinear kinematics and are solved by a two-step perturbation technique. The present analysis is validated through a direct comparison with those in the open literature. A parametric study is then performed to study the effects of GPL distribution pattern, weight fraction, geometry and size, temperature variation as well as the radius and initial velocity of the impactor on the low-velocity impact response of functionally graded GPLRC plates

Modeling the Stress-Induced Transformation Behavior of Shape Memory Alloys under Multiaxial Loading Conditions

A large number of criteria to model the onset of plasticity for ductile metals have been proposed by researchers in the last century. Strangely, very few researchers have tried to model the stress-induced crystalline phase transformation of Shape Memory Alloys (SMAs) according to yield criteria. This paper focuses on the question: is a yield criterion originally proposed for describing the plastic behavior of metals suitable to model the “pseudoelastic” behavior of SMAs? To answer this question, two yield criteria originally proposed by the present author are used to predict the initial surface of transformation onset of two different SMAs: Cu-Al-Be and Ni-Ti alloy. The predicted initial transformation onset surfaces of the two SMAs are compared with experimental results and existing theories reported in the literature and some significant conclusions and recommendations are given