Elastic behavior of glass-like functionally graded infinite hollow cylinder under hydrostatic loads using finite element method

A glass-like (viscoelastic) functionally graded cylinder is studied by using finite element method to investigate the mechanical responses. A subroutine is developed by using ANSYS parametric design language (APDL) to simulate two nonlinearities, which are the variation of material properties with respect to time and position. The cylinder is made of two different viscoelastic materials, namely, pure material one at inner and pure material two at outer surfaces. The material properties are assumed to be presented by simple power law distribution and moreover, bulk and shear moduli are varying with respect to time using the kernel functions depicted regarding Prony series. It is shown that the hoop stresses take the same values at the mean radius (middle of the thickness) for different values of time and grading index. It is found that the radial stress decreases to certain values for specific grading index and then by increasing the grading index it increases to maximum value that related to pure material cylinder. It is shown that unlike the zero axial stress in pure material cylinders, it varies along the thickness from minimum to maximum at inner and outer surfaces, respectively. It is concluded that the viscoelastic functionally graded (VFG) materials play an important role in steady and transient response of hollow cylinder under hydrostatic load.     

The effect of the aspect ratio of carbon nanotubes on their effective reinforcement modulus in an epoxy matrix

The potentiality of carbon nanotubes as reinforcement material is not only due to their exceptional high modulus, but also to their high aspect ratio. Indeed, the nanotubes contribution to the mechanical reinforcement in a polymer is strongly dependent on their distribution within the hosting matrix. In fact, the clustering of carbon nanotubes does limit the theoretical enhancement of the composite mechanical properties by a reduction of their effective aspect ratio.In this work, the reinforcement efficiency of carbon nanotubes having different aspect ratios has been experimentally investigated at low filler contents in an epoxy system. From a theoretical point of view, the classical theory (Cox, 1952 [25]) concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube-to-tube Random Contact Model (Philipse, 1996 [33]) which explicitly accounts for the progressive reduction of the tubes effective aspect ratio as the filler content increases. The validity of the proposed model was assessed by a comparison with available literature data, providing a good agreement.     

On the size-dependent behavior of functionally graded micro-beams

In this paper, the size-dependent static and vibration behavior of micro-beams made of functionally graded materials (FGMs) are analytically investigated on the basis of the modified couple stress theory in the elastic range. Functionally graded beams can be considered as inhomogeneous composite structures, with continuously compositional variation from usually a ceramic at the bottom to a metal at the top. The governing equations of motion and boundary conditions are derived on the basis of Hamilton principle. Closed-form solutions for the normalized static deflection and natural frequencies are obtained as a function of the ratio of the beam characteristic size to the internal material length scale parameter and FGM distribution functions of properties. The results show that the static deflection and natural frequencies developed by the modified couple stress theory have a significant difference with those obtained by the classical beam theory when the ratio of the beam characteristic size to the internal material length scale parameter is small.     

Enhancement and prediction of modulus of elasticity of palm kernel shell concrete

This paper presents results of an investigation conducted to enhance and predict the modulus of elasticity (MOE) of palm kernel shell concrete (PKSC). Scanning electron microscopic (SEM) analysis on palm kernel shell (PKS) was conducted. Further, the effect of varying sand and PKS contents and mineral admixtures (silica fume and fly ash) on compressive strength and MOE was investigated. The variables include water-to-binder (w/b) and sand-to-cement (s/c) ratios. Nine concrete mixes were prepared, and tests on static and dynamic moduli of elasticity and compressive strength were conducted.     

The modified couple stress functionally graded Timoshenko beam formulation

In this paper, a size-dependent formulation is presented for Timoshenko beams made of a functionally graded material (FGM). The formulation is developed on the basis of the modified couple stress theory. The modified couple stress theory is a non-classic continuum theory capable to capture the small-scale size effects in the mechanical behavior of structures. The beam properties are assumed to vary through the thickness of the beam. The governing differential equations of motion are derived for the proposed modified couple-stress FG Timoshenko beam. The generally valid closed-form analytic expressions are obtained for the static response parameters. As case studies, the static and free vibration of the new model are respectively investigated for FG cantilever and FG simply supported beams in which properties are varying according to a power law. The results indicate that modeling beams on the basis of the couple stress theory causes more stiffness than modeling based on the classical continuum theory, such that for beams with small thickness, a significant difference between the results of these two theories is observed.     

Maximum natural frequencies of polymer composite micro-beams by optimum distribution of carbon nanotubes

Optimum distribution of multi-walled carbon nanotubes (MWCNTs) within a polymer composite micro-beam is sought to achieve its highest natural frequencies given a weight percent (wt.%) of MWCNTs. To this end, the micro-beam is divided into ten segments which are perfectly bonded to their neighbors. Each segment is made of low-viscosity, thermosetting polyester epoxy/amine resin LY-5052 and is reinforced by MWCNTs. A computer program, written in the Python programming language, is compiled with ABAQUS to generate a three-dimensional (3D) finite element (FE) model of the micro-beam and subsequently to evaluate an optimum CNT distribution under various vibration modes and boundary conditions. The influence of uniform and optimum MWCNT distributions on the natural frequencies, mode shapes and equivalent stiffness of the micro-beams is investigated and the results are compared with those of the pure polymer micro-beam. Subsequently, after acquiring the optimum distribution of the MWCNTs, two new CNT dispersion functions are proposed for maximizing fundamental frequencies of the clamped-free and clamped–clamped micro-beams. The results of the FE analysis reveal that the optimal reinforcement distribution pattern significantly depends on vibration mode shapes, particularly the micro-beam curvature under each mode. It is observed that fundamental frequencies of clamped-free, clamped-guided and clamped–clamped micro-beams are enhanced up to 15.9%, 13.1% and 12.6%, respectively, by choosing optimum MWCNT distribution profiles along the micro-beam length.     

Determination of Young’s modulus in polyester-Al2O3 and epoxy-Al2O3 nanocomposites using the Digital Image Correlation method

Young’s modulus of nano-composite systems composed of unsaturated polyester and epoxy resins with alumina nanoparticles of different sizes has been experimentally estimated. The nanoparticles used were spherical alpha-Al₂O₃ having 30-40 and 200 nm in diameter. Young’s modulus was estimated using an inverse problem that is solved by means of the classical Levenberg-Marquardt technique. A cantilever beam under bending was used in the experiments and the experimental procedure was performed using the Digital Image Correlation method, which is a well-established optical-numerical method for estimating full-field displacement. Experimental results indicate that Young’s modulus increases with increasing nanoparticle volume fraction. Finally, the estimated Young’s moduli were compared with classical theoretical models, showing that the experimental results are in agreement with literature data.     

Characterizing mechanical properties of graphite using molecular dynamics simulation

The mechanical properties of graphite in the forms of single graphene layer and graphite flakes (containing several graphene layers) were investigated using molecular dynamics (MD) simulation. The in-plane properties, Young’s modulus, Poisson’s ratio, and shear modulus, were measured, respectively, by applying axial tensile stress and in-plane shear stress on the simulation box through the modified NPT ensemble. In order to validate the results, the conventional NVT ensemble with the applied uniform strain filed in the simulation box was adopted in the MD simulation. Results indicated that the modified NPT ensemble is capable of characterizing the material properties of atomistic structures with accuracy. In addition, it was found the graphene layers exhibit higher moduli than the graphite flakes; thus, it was suggested that the graphite flakes have to be expanded and exfoliated into numbers of single graphene layers in order to provide better reinforcement effect in nanocomposites.     

Prediction of Young’s modulus of graphene sheets and carbon nanotubes using nanoscale continuum mechanics approach

Analytical formulations are presented to predict the elastic moduli of graphene sheets and carbon nanotubes using a linkage between lattice molecular structure and equivalent discrete frame structure. The obtained results for a graphene sheet show an isotropic behavior, in contrast to limited molecular dynamic simulations. Young’s modulus of CNT represents a high dependency of stiffness on tube thickness, while dependency on tube diameter is more tangible for smaller tube diameters. The presented closed-form solution provides an insight to evaluate finite element models constructed by beam elements. The results are in a good agreement with published data and experimental results.     

Mechanical properties of silicone rubber composed of diverse vinyl content silicone gums blending

Silicone rubber composed of diverse vinyl content silicone gums blending were prepared and their mechanical properties were investigated. The silicone rubber composed of diverse vinyl content silicone gums blending whose crosslinking points were concentration distribution exhibited better tearing strength and higher tensile modulus in comparison with single vinyl content gums which were mean distribution. The average molecular weight (Mc) of the silicone rubber composed of diverse vinyl content blending are lower than that of single vinyl molar content 0.16% which was calculated by swelling equilibrium method. The viscoelastic behavior indicated the silicone rubber composed of 0.04% and 0.3% vinyl molar content gums blending possessed perfect flexibility at low temperature because it had the lowest glass transition temperature (T_g), and this sample had the largest storage modulus and loss modulus.     

Implementation of a constitutive model in finite element method for intense deformation

Since the constitutive information is one of the most important aspects of material deformation analysis, here a new constitutive model is proposed that can investigate the behavior of material during intense deformation better than existent models. The model that is completely based on physical mechanisms can predict all stages of flow stress evolution and also can elucidate the effects of strain and strain rate on flow stress evolution of material during intense plastic deformation. Here as an application, implementation of the constitutive model in finite element method (FEM) is used to compare two methods of sever plastic deformation (SPD) processes of copper sheet; repetitive corrugation and straightening (RCS) and constrained groove pressing (CGP). The modeling results are in good agreement with the experimental data and show that the hardness uniformity and its magnitude for RCSed sheet are higher than that for CGPed sheet. However, the prominence of these processes in strain uniformity depends on pass number.     

The effect of pre-softened wood chips on wood fibre aspect ratio and mechanical properties of wood–polymer composites

The objective of this work was to study the effect of chemical pre-treatment and moisture content of wood chips on the wood particle aspect ratio after compounding in a twin-screw extruder and on the mechanical properties of wood–polymer composites (WPCs). Composites with 50 wt.% wood content were manufactured using pre-treated and untreated wood chips. The effect of wood moisture content on composite properties was studied by using dried and undried wood chips. The mechanical properties and fracture surfaces of the composites as well as the microstructure and aspect ratio of wood particles after compounding were studied. The highest wood particle aspect ratio after extrusion was achieved by using pre-treated, undried wood chips as raw material. The chemical pre-treatment was found to enhance the defibration of wood chips as well as the mechanical properties of the composites.     

A negative Poisson’s ratio carbon fibre composite using a negative Poisson’s ratio yarn reinforcement

The manufacture of negative Poisson’s ratio (auxetic) composites, containing inherently auxetic phases is rare and has been confined to relatively low modulus composite systems with stiffnesses several orders of magnitude below those of structural composites. This paper presents the use of an auxetic double helix yarn that is used to produce a unidirectional fibre composite with both relatively high stiffness (4 GPa) and negative Poisson’s ratio (−6.8), at 30% fibre volume fraction, compared to other auxetic composites. This is the first structural auxetic composite to be produced using carbon fibre and importantly it was produced using standard manufacturing techniques and therefore is potentially applicable in a variety of engineering applications.     

Influence of stress softening on energy-absorption capability of polymeric foams

The energy-absorption capability of the polymeric foam used in vehicle bumpers is investigated through cyclic loading tests in different loading types, including uniaxial compression, biaxial compression and three-point bending. The test results indicate, due to significant stress softening, the energy-absorption capability of the bumper foam is greatly reduced after it is repeatedly loaded from the raw state. It is also revealed that both the softening effect and the reduction of energy-absorption are dependent on the deformation history. To account for the softening effect as well as its dependence on deformation history in simulation of the bumper foam, appropriate material models are identified and a modeling approach is developed. Using consecutive low-speed impact tests on a bumper system, the influence of the stress softening on the structural performance is studied. Both the experimental and modeling results indicate that the stress softening of the foam cushion compromises to a certain extent the bumper impact performance in subsequent impacts.     

Mechanical properties of hybrid composites using finite element method based micromechanics

A micromechanical analysis of the representative volume element of a unidirectional hybrid composite is performed using finite element method. The fibers are assumed to be circular and packed in a hexagonal array. The effects of volume fractions of the two different fibers used and also their relative locations within the unit cell are studied. Analytical results are obtained for all the elastic constants. Modified Halpin–Tsai equations are proposed for predicting the transverse and shear moduli of hybrid composites. Variability in mechanical properties due to different locations of the two fibers for the same volume fractions was studied. It is found that the variability in elastic constants and longitudinal strength properties was negligible. However, there was significant variability in the transverse strength properties. The results for hybrid composites are compared with single fiber composites.     

Transient and thermal contact analysis for the elastic behavior of functionally graded brake disks due to mechanical and thermal loads

In this paper, the transient and contact analysis of functionally graded (FG) brake disk is presented. The analysis was carried out using ANSYS parametric design language (APDL). The FG brake disk is made of metal–ceramic material. The material properties vary in radial direction with the values from full-metal at the inner radius to that of full-ceramic at the outer radius. In the analysis, FG brake disk is in contact with one pure pad disk and coulomb contact friction is considered as heat source. The non-dimensional results are obtained for specific value of grading index (n = 1) by considering different material property divisions of 25, 50, 100 and 200. The results presented are for the pressure distribution, total stress, pad penetration, friction stress, heat flux and temperature during contact, for different values of contact stiffness factor, F_kn, which depends on the property gradation of FG brake disk with 200 material property divisions. The results show that the contact pressure and contact total stress increase with increasing values of F_kn, and hence it can be concluded that gradation of the metal–ceramic has significant effect in the thermomechanical response of FG brake disks.     

Numerical analysis of panels’ dent resistance considering the Bauschinger effect

The Bauschinger effect should be considered in the analysis of panels’ dent resistance, because sheet metal experiences a complex loading history from stamping to denting. This paper studies the modeling and simulation of panels’ static dent resistance, taking the Bauschinger effect into consideration. Our work covers two parts: simulation and experiment. Procedures of drawing, springback I, indenting and springback II are simulated in a multiple step analysis. Different hardening models, including the isotropic hardening model, the linear kinematic hardening model and the nonlinear combined hardening model are used, respectively, in simulation. Comparing the simulation results with the experiment results, we find that the Bauschinger effect has a great influence on panels’ dent resistance. When panels are made of high strength steel or stamped with a high Blank Holder Force (BHF), the Bauschinger effect on panels’ dent resistance is more severe. Considering the effect in numerical analysis would improve the simulation accuracy effectively. The work of this paper is beneficial to material selection and processing optimization for automobile exterior panels.     

The effective Young’s modulus of composites beyond the Voigt estimation due to the Poisson effect

The Voigt estimation or the rule of mixture has been believed to be the upper bound of the effective Young’s modulus of composites. However, this is only true in the situations where the Poisson effect is not significant. In this paper, we accurately derived the effective compliance matrix for two-phase layered composites by accounting for the Poisson effect. It is interesting to find that the effective Young’s modulus in both transverse and longitudinal direction can exceed not only the Voigt estimation, but also the Young’s modulus of the stiffest constituent phase. Moreover, the longitudinal (or parallel connection) Young’s modulus is not always larger than the transverse (or serial connection) one. For isotropic composites, it has also been demonstrated that the Voigt estimation is not the upper bound for the effective Young’s modulus. Therefore, one should be careful in applying the well known bound estimations on the effective Young’s modulus of composites if one of the phases is near its incompressibility limit.     

The manufacture and characterisation of a novel,low modulus,negative Poisson’s ratio composite

Relatively few negative Poisson’s ratio (auxetic) composites have been manufactured and characterised and none with inherently auxetic phases [Milton G. J. Mech. Phys. Solids 1992;40:1105–37]. This paper presents the use of a novel double-helix yarn that is shown to be auxetic, and an auxetic composite made from this yarn in a woven textile structure. This is the first reported composite to exhibit auxetic behaviour using inherently auxetic yarns. Importantly, both the yarn and the composite are produced using standard manufacturing techniques and are therefore potentially useful in a wide range of engineering applications.     

Young’s moduli of functionalized single-wall carbon nanotubes under tensile loading

This paper quantitatively investigates the effect of chemical functionalization on the axial Young’s moduli of single-walled carbon nanotubes (SWCNTs) based on molecular mechanics (MM) simulation, in which the COMPASS force field is used to model the interatomic interactions in a nonfunctionalized nanotube or a functionalized nanotube grafted with vinyl groups. We obtain the axial Young’s moduli of both functionalized and nonfunctionalized SWCNTs. The influences of the number and distribution density of the sp³-hybridized carbon atoms and the radius and chirality of the SWCNTs on Young’s moduli are studied. The results indicate that Young’s moduli depend strongly on the chirality of the SWCNTs and the distribution density of the sp³-hybridized carbon atoms. A 37.50% content of sp³-hybridized carbon atoms may degrade Young’s modulus by up to 33.36%. In addition, MM simulations show that the functionalization of SWCNTs results in a decrease of Young’s moduli of the corresponding SWCNT/polyethylene composites.