Volume Fractions Of Constituents Research Articles

On vibration of functionally graded sandwich nanoplates in the thermal environment

This paper deals with the free vibration response of rectangular functionally graded material sandwich nanoplates with simply supported boundary conditions. The material properties of the FGM layers are temperature-dependent and supposed to be graded continuously along the thickness direction. A simple power-law distribution in terms of the volume fractions of the material constituents is employed to obtained the effective material properties. Eringen’s nonlocal elasticity model is incorporated in order to take into account the small size effects. Two types of functionally graded material sandwich nanoplates are considered: a sandwich with functionally graded material face layers and homogeneous core, and a sandwich with homogeneous face layers and functionally graded material core. The equations of motion of the functionally graded material sandwich nanoplates are derived by using the higher shear deformation theory and the Hamilton’s variational principle, and solved using the Navier’s solutions. Several numerical results indicate the influence of the power–law index, the nonlocal parameter, the geometrical parameters of the nanoplate, and the temperature variation on the free vibration response are presented.

Free Vibration Response of Four-Parameter Functionally Graded Thick Spherical Shell Formulation on Higher Order Shear Deformation Theory

This paper emphasizes on the free vibration (FV) responses of functionally graded thick spherical shell in rectangular form using traditional mathematical formulation on finite element method and governed by Higher order shear deformation theory (HOSDT). A functionally graded spherical shell made up of metal-rich on the top surface and in contrast, base surface of the model is ceramic-rich. The FG volume fraction of four-parameter power-law material constituents assumed in the thickness direction. To highlight the potential for the current method, convergence studies, and validation tests performed to establish the stability and accuracy attained by the current approach. The parametric studies presented to scrutinize the influence of choice of four parameters employed through power-law distribution. The eminence effect of spherical shell geometrical properties, and different types of support conditions, skew angle on the FV behavior of non-dimensional frequency responses examined in detail.

The best grading pattern selection for the axisymmetric elastic response of pressurized inhomogeneous annular structures (sphere/cylinder/annulus) including rotation

Many models were offered in the literature to simulate the material gradation patterns within the functionally graded metal-ceramic structures. The present study provides a comprehensive and comparative numerical examination of the displacement and stress distributions in the three types of annular structures, namely spheres, cylinders, and annuli by gathering most of models up. To this end, an efficacious and accurate numerical method, the complementary functions method, is exploited in the numerical determination of the elastic fields with several material-grading patterns under internal pressure including centrifugal forces to search the best one exhibiting desired elastic axisymmetric behavior of such structures. A functionally graded material, viz., a particle reinforced composite, is assumed to be composed of an aluminum oxide (ceramic/Al2O3) and a stainless steel (metal/SUS-410). Different grading patterns are formed by using several material grading rules such as a simple power rule, an exponential rule, a linear function, a Voigt mixture with power of volume fractions of constituents, a Mori–Tanaka scheme, Chung and Chi’s Sigmoid function, Chen and Lin’s sine rule, Dryden and Jayaraman’s combined power and exponential rule, and finally Tornabene’s four-parameter symmetric/asymmetric power functions. Variation of the elastic fields is presented in both tabular and graphical forms. Combined effects of both the pressure and rotation are also studied for cylinders and annuli having aspect ratios of 0.6 and 0.9. It is observed in the chosen patterns that a pattern with gradually increasing ceramic constituents toward a full ceramic layer at the outer surface is found as the best under pressure loads. Combined pressure plus centrifugal forces require a pattern having a full ceramic layer at the inner surface following a decreasing pattern with ceramic constituent toward the outer surface. The results with plain stress assumption are found somewhat higher than the results with generalized plane strain. As expected, the spheres have significantly smallest elastic fields than the others under the same pressure loads and aspect ratios.

Nonlinear and post-buckling responses of FGM plates with oblique elliptical cutouts using plate assembly technique

The aim of this study is to obtain the nonlinear and post-buckling responses of relatively thick functionally graded plates with oblique elliptical cutouts using a new semi-analytical approach. To model the oblique elliptical hole in a FGM plate, six plate-elements are used and the connection between these elements is provided by the well-known Penalty method. Therefore, the semi-analytical technique used in this paper is known as the plate assembly technique. In order to take into account for functionality of the material in a perforated plate, the volume fraction of the material constituents follows a simple power law distribution. Since the FGM perforated plates are relatively thick in this research, the structural model is assumed to be the first order shear deformation theory and Von-Karman\'s assumptions are used to incorporate geometric nonlinearity. The equilibrium equations for FGM plates containing elliptical holes are obtained by the principle of minimum of total potential energy. The obtained nonlinear equilibrium equations are solved numerically using the quadratic extrapolation technique. Various sets of boundary conditions for FGM plates and different cutout sizes and orientations are assumed here and their effects on nonlinear response of plates under compressive loads are examined.

Free vibration behavior of corrugated functionally graded composite panel

Abstract In this work, free vibration behaviour of sinusoidally corrugated functionally graded composite panel is examined. In this analysis, the functionally graded panel is comprised of metal at the bottom surface and ceramic at the top surface, and metal/ceramic phase between the top and bottom surfaces of the panel. The effective material properties of in-homogenous functionally graded material are obtained using simple rule-of-mixture, whereas the volume fractions of each material constituents are computed through the power-law distribution. The corrugated panel is modelled and analysed via finite element tool (ANSYS APDL) using eight-noded shell element (SHELL281). The displacement field is expressed using first-order shear deformation theory with six degrees-of-freedom. The Block-Lanczos method is employed to obtain the free vibration responses of the corrugated panel. The accuracy of the present model is exhibited through the comparison study in which the present results are compared with the previously reported results. In addition, numerous examples are illustrated to demonstrate the influences of various geometrical and material parameters, such as side-to-thickness ratio, corrugation, aspect ratio and power-law index, and support conditions on the free vibration behaviour of corrugated panel

A new innovative 3-unknowns HSDT for buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions

In this study a new innovative three unknowns trigonometric shear deformation theory is proposed for the buckling and vibration responses of exponentially graded sandwich plates resting on elastic mediums under various boundary conditions. The key feature of this theoretical formulation is that, in addition to considering shear deformation effect, it has only three unknowns in the displacement field as in the case of the classical plate theory (CPT), contrary to five as in the first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). Material characteristics of the sandwich plate faces are considered to vary within the thickness direction via an exponential law distribution as a function of the volume fractions of the constituents. Equations of motion are obtained by employing Hamilton\'s principle. Numerical results for buckling and free vibration analysis of exponentially graded sandwich plates under various boundary conditions are obtained and discussed. Verification studies confirmed that the present three -unknown shear deformation theory is comparable with higher-order shear deformation theories which contain a greater number of unknowns.

Extrafibrillar matrix yield stress and failure envelopes for mineralised collagen fibril arrays

Bone metabolic diseases such as osteoporosis constitute a major socio-economic challenge. A detailed understanding of the structure-property relationships of bone's underlying hierarchical levels has the potential to improve diagnosis and the ability to treat those diseases, especially with regards to the onset of failure. Therefore, elastic and yield properties of mineralised turkey leg tendon (MTLT), a mineralised tissue that is similar to bone but has a simpler multiscale structure, were investigated. Elastic properties were identified using a multiscale micromechanical model. The input parameters include constituent mechanical properties, volume fractions and inclusion aspect ratios and these were obtained from a wide variety of literature sources. The determined elastic properties were used to formulate micromechanically informed yield surfaces and to identify yield properties of MTLT at the nanometre length scale where failure is first reported to occur. This was done in conjunction with experimental results from the compression of micropillars extracted from individual mineralised collagen fibres. This data was then used to identify micromechanically informed failure envelopes. The shear yield stress of the extrafibrillar matrix, associated with interfibrillar sliding, was identified as 137.65 MPa. The ratio between tensile and compressive yield stress in the Drucker-Prager yield criterion was 0.65. For both criteria apparent yield stress of the mineralised collagen fibril decreased to 25.3–31.4% when varying fibril orientation from 0° to 90°. This study identified yield properties of extrafibrillar matrix using an aligned mineralised tissue. The ability to obtain yield stress data and unloading stiffness from micropillar compression tests of MTLT at the level of the mineralised collagen fibril array and downscaling these into the EM mitigates against possible errors associated with macroscopic stiffness predictions and proved to be an invaluable advantage compared to similar modelling approaches. Results may help to improve computational models that may then be used in pre-clinical testing or development of personalised treatment strategies.

A phenomenological approach to study the nonlinear magnetoelectric (ME) response of ME composites

Magnetoelectric (ME) composites have recently attracted many researchers because of their significant applications in devices like sensors, energy harvesters etc. In this work, a unique phenomenological nonlinear constitutive model for ferromagnetic material has been developed and further, this model is extended to study the ME coupling coefficient of ME composites. The proposed model is based on metal plasticity approach for ferromagnetic material and is also thermodynamically consistent. A robust non-iterative scheme has been proposed and the developed model is incorporated into the computational scheme which renders computationally efficient simulations. In order to validate the proposed model, firstly, a press fit assembly of ME composite has been considered. The prestress developed due to the press fit is numerically evaluated using ABAQUS. The simulated results for the press fit configuration are compared with the experimental observations. To illustrate the generality of this model, a layered ME composite configuration has also been studied. Finally, a parametric study has been conducted and the influence of volume fraction of constituents, boundary conditions and the aspect ratio for the press fit ME composite assembly are reported.

New mean-field homogenization schemes for the constitutive modelling of the elastic and elastoplastic deformation behavior of multi-phase materials

In this study, a new class of mean-field homogenization (MFH) models were developed based on the underlying concepts of the direct and inverse Mori-Tanaka and Lielens MFH schemes. The proposed models were employed to predict the elastic and elastoplastic constitutive responses for a range of representative multi-phase materials, including polymer- and metal-matrix composites and a dual-phase steel. To evaluate the performance of the developed MFH models in the elastic region, their predictions for the elastic constants of graphite-reinforced epoxy, Al2O3-reinforced AA7075, and TiB2-reinforced AISI 1045 steel with different ellipsoidal-inclusion shapes and volume fractions were compared with the results of unit-cell finite element method (FEM) simulations under uniaxial-tension loading. For the plastic region, the proposed MFH models were coupled with various linearization approaches, including the first-order secant-based and tangent-based schemes, to estimate the flow behavior of DP590 steel in uniaxial tension. The MFH predictions were shown to compare favorably with the results of unit-cell FEM simulations and experiment. Moreover, the predictive ability of the developed models for both elastic and plastic responses was assessed via comparisons with the approximations of the self-consistent and Mori-Tanaka MFH models. The results showed that the proposed MFH models can describe the elastic and elastoplastic behavior of heterogeneous materials with different constituent volume fractions as well as or better than conventional MFH models.

Modeling the thermal and soot oxidation dynamics inside a ceria-coated gasoline particulate filter

Gasoline particulate filters (GPFs) are practically adoptable devices to mitigate particulate matter emissions from vehicles using gasoline direct ignition engines. This paper presents a newly developed control-oriented model to characterize the thermal and soot oxidation dynamics in a ceria-coated GPF. The model utilizes the GPF inlet exhaust gas temperature, exhaust gas mass flow rate, the initial GPF soot loading density, and air–fuel ratio to predict the internal GPF temperature and the amount of soot oxidized during regeneration events. The reaction kinetics incorporated in the model involve the rates of both oxygen- and ceria-initiated soot oxidation reactions. Volumetric model parameters are calculated from the geometric information of the coated GPF, while the air–fuel ratio is used to determine the volume fractions of the exhaust gas constituents. The exhaust gas properties are evaluated using the volume fractions and thermodynamic tables, while the cordierite specific heat capacity is identified using a clean experimental data set. The enthalpies of the regeneration reactions are calculated using thermochemical tables. Physical insights from the proposed model are thus enhanced by limiting the number of parameters obtained from fitting to only those which cannot be directly measured from experiments. The parameters of the model are identified using the particle swarm optimization algorithm and a cost function designed to simultaneously predict both thermal and soot oxidation dynamics. Parameter identification and model validation are performed using independent data sets from laboratory experiments conducted on a ceria-coated GPF. This work demonstrates that the proposed model can be successfully implemented to predict ceria-coated GPF dynamics under different soot loading and temperature conditions.

Effect of nonlinear elastic foundations on dynamic behavior of FG plates using four-unknown plate theory

This present paper concerned with the analytic modelling for vibration of the functionally graded (FG) plates resting on non-variable and variable two parameter elastic foundation, based on two-dimensional elasticity using higher shear deformation theory. Our present theory has four unknown, which mean that have less than other higher order and lower theory, and we denote do not require the factor of correction like the first shear deformation theory. The indeterminate integral are introduced in the fields of displacement, it is allowed to reduce the number from five unknown to only four variables. The elastic foundations are assumed a classical model of Winkler-Pasternak with uniform distribution stiffness of the Winkler coefficient (kw), or it is with variables distribution coefficient (kw). The variable\'s stiffness of elastic foundation is supposed linear, parabolic and trigonometry along the length of functionally plate. The properties of the FG plates vary according to the thickness, following a simple distribution of the power law in terms of volume fractions of the constituents of the material. The equations of motions for natural frequency of the functionally graded plates resting on variables elastic foundation are derived using Hamilton principal. The government equations are resolved, with respect boundary condition for simply supported FG plate, employing Navier series solution. The extensive validation with other works found in the literature and our results are present in this work to demonstrate the efficient and accuracy of this analytic model to predict free vibration of FG plates, with and without the effect of variables elastic foundations.

Effect of Temperature Dependency on Thermoelastic Behavior of Rotating Variable Thickness FGM Cantilever Beam

Thermoelastic behavior of temperature-dependent (TD) and independent (TID) functionally graded variable thickness cantilever beam subjected to mechanical and thermal loadings is studied based on shear deformation theory using a semi-analytical method. Loading is composed of a transverse distributed force, a longitudinal distributed temperature field due to steady-state heat conduction from root to the tip surface of the beam and an inertia body force due to rotation. A successive relaxation (SR) method for solving temperature-dependent steady-state heat conduction equation is employed to obtain the accurate temperature field. The beam is made of functionally graded material (FGM) in which the mechanical and thermal properties are variable in longitudinal direction based on the volume fraction of constituent. Using first-order shear deformation theory, linear strain–displacement relations and Generalized Hooke’s law, a system of second order differential equation is obtained. Using division method, differential equations are solved for every division. As a result, longitudinal displacement, transverse displacement, and consequently longitudinal stress, shear stress and effective stress are investigated. The results are presented for temperature dependent and independent properties. It has been found that the temperature dependency of the material has a significant effect on temperature distribution, displacements and stresses. This model can be used for thermoelastic analysis of simple turbine blades.

Nonlinear free vibration analysis of functionally graded beams by using different shear deformation theories

This study investigates the nonlinear free vibration of functionally graded material (FGM) beams by different shear deformation theories. The volume fractions of the material constituents and effective material properties are assumed to be changing in the thickness direction according to the power-law form. The von Kármán geometric nonlinearity has been considered in the formulation. The Ritz method and Lagrange equation are adopted to yield the discrete formulations. A direct numerical integration method for the motion equation in matrix form is developed to solve the nonlinear frequencies of FGM beams. Comparing with the global concordant deformation assumption (GCDA), a new deformation assumption named as local concordant deformation assumption (LCDA) is proposed in this study. The LCDA fits with the real deformation of the vibrating beam better, thus more accurate results of the nonlinear frequency can be expected. In numerical results, the comparison study of the GCDA and LCDA is carried out. In addition, the effects of power-law index, slenderness ratio and maximum deflection for different shear deformation theories and boundary conditions on the nonlinear frequency of the beam are discussed.

Nonlinear vibration of FGM moderately thick toroidal shell segment within the framework of Reddy’s third order-shear deformation shell theory

Nonlinear vibration and dynamic response of functionally graded moderately thick toroidal shell segments resting on Pasternak type elastic foundation are investigated in this paper. Functionally graded materials are made from ceramic and metal, and the volume fraction of constituents are assumed to vary through the thickness direction according to a power law function. Reddy’s third order shear deformation, von Karman nonlinearity, Airy stress function method and analytical solutions are used to derive the governing equations. Galerkin method is used to convert the governing equation into nonlinear differential equation, then the explicit expressions of natural frequencies and nonlinear frequency–amplitude relations are obtained. Using Runge–Kutta method, the nonlinear differential equation of motion is solved, and then nonlinear vibration and dynamic response of shells are analyzed. The effects of temperature, material and geometrical properties, and foundation parameters on nonlinear vibration and dynamic characteristics are investigated and discussed in detail.

Analytical solution for free vibration of stiffened functionally graded cylindrical shell structure resting on elastic foundation

In this work, the analytical solution for free vibration of functionally graded cylindrical shell with stiffeners resting on Winkler–Pasternak foundation with several boundary conditions is reported. Material properties of the cylindrical shell are assumed to be varying smoothly and continuously across the thickness according to the power law distribution of the volume fraction of constituents. The governing equations of the stiffened functionally graded cylindrical shell resting on elastic foundation are obtained by using Hamilton’s principle, the first-order shear deformation theory and the Lekhnitsky smeared stiffeners technique. The purpose of the present study is to illustrate a simple approach to get the natural frequency of the stiffened functionally graded cylindrical shell with several boundary conditions by using the Galerkin method with beam functions of the axial displacement fields. A good agreement is obtained as the present results in comparison with those of publications in the existing literature. In numerical investigations, some influences of volume fraction index, cylindrical shell’s geometric ratios, boundary conditions and elastic foundation parameters on the fundamental frequency of the stiffened cylindrical shell resting on elastic foundation are given.

Assessment of anisotropic mechanical properties of a 3D printed carbon whisker reinforced composite

A commercial carbon whisker reinforced polylactic acid composite made by a type of three-dimensional (3D) printing known as material extrusion additive manufacturing is investigated. The primary objective is to experimentally characterize and model the direction-dependent tensile modulus of elasticity of unidirectionally printed composite material to assess the degree of anisotropy induced during printing and to determine how well the measured properties can be predicted by multiscale mechanics-based models. The model predictions are based on microstructural characteristics such as the aspect ratio and orientation of the whiskers and the constituent volume fractions. Other material characteristics are assumed, such the cylindrical shape of voids in the matrix and the perfect bonding condition of the whiskers. The experiments indicate (1) that the modulus in the 0-deg. printed direction can be at least twice the modulus in the 90-deg. printed direction and (2) that whisker alignment is improved during printing. Two models accounting for imperfect whisker alignment are used to predict the modulus of the 0-deg. material reasonably well, although the 90-deg. modulus is over-predicted by both models. The 0-deg. direction is roughly two times stronger than the 90-deg. direction in tension.

Free vibrations and static analysis of functionally graded sandwich plates with three-dimensional finite elements

A three-dimensional modelling of free vibrations and static response of functionally graded material (FGM) sandwich plates is presented. Natural frequencies and associated mode shapes as well as displacements and stresses are determined by using the finite element method within the ABAQUS™ code. The three-dimensional (3-D) brick graded finite element is programmed and incorporated into the code via the user-defined material subroutine UMAT. The results of modal and static analyses are demonstrated for square metal-ceramic functionally graded simply supported plates with a power-law through-the-thickness variation of the volume fraction of the ceramic constituent. The through-the-thickness distribution of effective material properties at a point are defined based on the Mori-Tanaka scheme. First, exact values of displacements, stresses and natural frequencies available for FGM sandwich plates in the literature are used to verify the performance and estimate the accuracy of the developed 3-D graded finite element. Then, parametric studies are carried out for the frequency analysis by varying the volume fraction profile and value of the ceramic volume fraction.

Numerical analysis for free vibration of functionallygraded beams using an original HSDBT

This work presents a free vibration analysis of functionally graded beams by employing an original high order shear deformation theory (HSDBT). This theory use only three unknowns, but it satisfies the stress free boundary conditions on the top and bottom surfaces of the beam without requiring any shear correction factors. The mechanical properties of the beam are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. In order to investigate the free vibration response, the equations of motion for the dynamic analysis are determined via the Hamilton

The role of patch hybridization on tensile response of cracked panel repaired with hybrid composite patch: experimental and numerical investigation

ABSTRACT This article presents a distinct perspective of structural repair by bonding the hybrid composite patch. A novel hybrid composite patch is prepared from the carbon and glass fibers to repair the cracked panel. Different volume fractions of constituents are maintained to prepare the composite patch with varying stiffness. The elastic constant of the composite patch is derived by applying the rule of hybrid mixture and modified Halpin Tsai equation. The stress intensity factor in the panel and interfacial stresses in the adhesive layer are evaluated to assess repair efficiency and repair durability. Effects of the elastic modulus of the adhesive on the performance of composite patch repair are demonstrated. The load carrying capacity and failure strength are examined for variation in patch stiffness. The disbonded surface morphology is investigated through scanning electron microscopy after failure. The results reveal that the hybrid composite patch provided sufficient reinforcement to reduce the stress intensity and interfacial stresses. Patch hybridization has offered a pragmatic solution and proposed as an alternative patch material to repair the cracked structure.

Study on axial resonance magneto-electric (ME) effects of layered magneto-electric composites

An experimental investigation has been carried out to capture the magneto-mechanical behavior and material parameters of magnetostrictive material. Further, the experimental study is extended to capture the magnetoelectric (ME) coupling response of trilayered composites by applying both alternating and static magnetic fields. From the experiments, it is observed that the magnetostrictive material has a nonlinear hysteretic behavior. Hence, a three dimensional (3-D) nonlinear constitutive model has been proposed based on a thermodynamic framework and multisurface plasticity. In ME composites, it is also observed that a large ME coupling response can be obtained while operating near resonance frequencies. To capture the resonant ME effects, a theoretical formulation has been proposed based on axial vibrations theory and the proposed constitutive model has been incorporated in the formulation. The simulated resonant ME coupling response based on the proposed formulation is compared with the experimental data and found to be in agreement with each other. Further, a parametric study has been performed to address the variation of the resonant ME response as a function of various parameters such as axial compliance ratio, volume fraction of constituents, temperature, direction of magnetic loading and aspect ratio. This study reveals that the coupling response can be optimized by choosing the suitable parameters based on design requirement.