Shear Constants Research Articles

Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions

In this research, the nonlinear static, buckling and vibration analysis of viscoelastic micro-composite beam reinforced by various distributions of boron nitrid nanotube (BNNT) with initial geometrical imperfection by modified strain gradient theory (MSGT) using finite element method (FEM) are presented. The various distributions of BNNT are considered as UD, FG-V and FG-X and also, the extended rule of mixture is used to estimate the properties of micro-composite beam. The components of stress are dependent to mechanical, electrical and thermal terms and calculated using piezoelasticity theory. Then, the kinematic equations of micro-composite beam using the displacement fields are obtained. The governing equations of motion are derived using energy method and Hamilton\'s principle based on MSGT. Then, using FEM, these equations are solved. Finally the effects of different parameters such as initial geometrical imperfection, various distributions of nanotube, damping coefficient, piezoelectric constant, slenderness ratio, Winkler spring constant, Pasternak shear constant, various boundary conditions and three material length scale parameters on the behavior of nonlinear static, buckling and vibration of micro-composite beam are investigated. The results indicate that with an increase in the geometrical imperfection parameter, the stiffness of micro-composite beam increases and thus the non-dimensional nonlinear frequency of the micro structure reduces gradually.

Molecular Dynamics Simulation of Diffusion of Fe in HCP Ti Lattice

Diffusion of a single Fe atom in a defect free hcp Ti lattice was studied using molecular dynamics (MD) simulation. Modified Embedded Atom Method potentials derived by Sa et al. (Scripta Mater 59:595, 2008) were used for carrying out the MD simulations. These potentials were verified by estimating the physical properties of the Fe–Ti system such as cohesive energy, bulk modulus and the shear constants. Fe atom trajectory in Ti lattice was traced in the temperature range of 500–900 °C. Diffusivity of Fe ( $$ D_{Fe} $$ ) atom in Ti lattice was obtained from the estimation of mean square displacement for total time of simulation at each temperature. $$ D_{Fe} $$ at 900 °C was obtained as 7.784 × 10−15 m2/s. From the Arrhenius analysis of $$ \ln D_{Fe} $$ versus temperature, the activation energy required for the diffusion of Fe atom in hcp Ti lattice was obtained as 117 kJ/mol.

First principles study of ceramic materials (IVB group carbides) under ultrafast laser irradiation**Project supported by the National Natural Science Foundation of China (Grant Nos. 11474207 and 11374217).

Group IVB carbides have been applied in extreme aerospace environments as hard ceramic coatings; ZrC is being considered as a replacement for SiC in nuclear reactors. Therefore, a thorough understanding of the laser irradiation response of group IVB carbides is of clear significance. However, the existing knowledge on the fundamental properties of IVB group carbides is limited and insufficient with regard to both irradiated and non-irradiated characteristics. We investigate the effect of ultrafast laser irradiation on the lattice stability of ceramic materials (IVB group carbides) using the density functional perturbation theory (DFPT). The calculated phonon frequencies of TiC and ZrC at the ground state are in good agreement with previous calculations and experimental values. The phonon frequencies of IVB group carbides are positive, even though the electronic temperature reached 5 eV. Thus, IVB group carbides are more stable under ultrafast laser irradiation, which has greater benefits in nuclear and aeronautical applications compared to metals (W, Na), semimetals (Bi), and semiconductors (Si, SiC). The thermodynamic properties of ZrC are calculated as functions of their lattice temperature at different electronic temperatures. The elastic shear constants of IVB group carbides satisfy the Born stability criteria at Te = 5 eV. In addition, a comparison of the predicted melting temperatures of IVB group carbides, reveal that HfC is better suited for extreme high-temperature environments.

Investigation of elastic moduli and constants of zinc-blende Al y Ga1-yAs alloy by statistical moment method

The elastic moduli and elastic constants of the ternary semiconductor alloy Al y Ga1-yAs at finite temperature have been investigated using the statistical moment method. The Young, shear, bulk moduli and elastic constants C11, C12, C44 of the zinc-blende Al y Ga1−yAs crystal are calculated as functions of Al composition and temperature. Numerical calculations have been performed and compared with those of the experimental and other theoretical results showing the reasonable agreements. Our study shows that elastic moduli and C11, C12 constants of zinc-blende Al y Ga1−yAs alloy are decreasing functions of the temperature and Al composition; C44 constant is a decreasing function of the Al composition.

Buckling and reliability analysis of CNT-reinforced-beams based on Hasofer-Lind and Rackwitz-Fiessler methods

In this paper, the nonlinear conjugate map based on the conjugate Rackwitz-Fiessler and Hasofer-Lind (CHL-RF) method is used to evaluate the reliability using first order reliability method of the embedded nanocomposite beam, which is made from polymer reinforced with carbon nanotubs (CNTs). The structure is simulated with Timoshenko beam model. The Mori-Tanaka method is applied for obtaining the effective properties of nanocomposite beam. The surrounding elastic medium is considered by spring and shear constants. Utilising energy method and Hamilton's principal, the governing equations are obtained. Using an analytical method, the buckling performance function of structure is obtained. The influences of the basic random variables including the length to thickness ratio of beam (L/h), spring constant and shear constant of foundation with respect to the volume fraction of CNTs are investigated on the reliability index of the nanocomposite beam subjected to axial force of 20 GPa. The results indicated that the failure probabilities of the studied the nanocomposite beam are the sensitive to the length to thickness of beam (L/h) and spring constant of foundation variables.

Three-body interactions and the elastic constants of hcp solid 4He.

The effect of three-body interactions on the elastic properties of hexagonal close packed solid 4He is investigated using variational path integral (VPI) Monte Carlo simulations. The solid's nonzero elastic constants are calculated, at T = 0 K and for a range of molar volumes from 7.88 cm3/mol to 20.78 cm3/mol, from the bulk modulus and the three pure shear constants C0, C66, and C44. Three-body interactions are accounted for using our recently reported perturbative treatment based on the nonadditive three-body potential of Cencek et al. Previous studies have attempted to account for the effect of three-body interactions on the elastic properties of solid 4He; however, these calculations have treated zero point motions using either the Einstein or Debye approximations, which are insufficient in the molar volume range where solid 4He is characterized as a quantum solid. Our VPI calculations allow for a more accurate treatment of the zero point motions which include atomic correlation. From these calculations, we find that agreement with the experimental bulk modulus is significantly improved when three-body interactions are considered. In addition, three-body interactions result in non-negligible differences in the calculated pure shear constants and nonzero elastic constants, particularly at higher densities, where differences of up to 26.5% are observed when three-body interactions are included. We compare to the available experimental data and find that our results are generally in as good or better agreement with experiment as previous theoretical investigations.

Optimization of dynamic buckling for sandwich nanocomposite plates with sensor and actuator layer based on sinusoidal-visco-piezoelasticity theories using Grey Wolf algorithm

Optimization of embedded piezoelectric sandwich nanocomposite plates for dynamic buckling analysis is presented in this work based on Grey Wolf algorithm. The Grey Wolf algorithm mimics the leadership hierarchy and hunting mechanism of grey wolves in nature. In addition, the main steps of hunting, searching for prey, encircling prey, and attacking prey are employed. The structure is composed of a laminated functionally graded-carbon nanotubes reinforced layers as core integrated with sensor and actuator layers considering structural damping effects. Two-dimensional magnetic and 3D electric fields are applied to core and piezoelectric layers, respectively. Sinusoidal shear deformation theory is utilized for obtaining the motion equations and differential quadrature method is applied for solution. Also, a proportional–derivative controller is employed to control the dynamic behavior of the structure. Finally, the optimum designs for the structure are evaluated using proposed Grey Wolf algorithm based on the geometrical parameters of plate, applied voltage, controller parameters, volume fraction of carbon nanotubes, spring, and shear constants of foundation. Numerical results indicate that by applying the positive voltage and transverse magnetic field the optimum dimensionless frequency of the system decreases.

Dynamic stability of FG-CNT-reinforced viscoelastic micro cylindrical shells resting on nonhomogeneous orthotropic viscoelastic medium subjected to harmonic temperature distribution and 2D magnetic field

This paper deals with the dynamic stability of embedded functionally graded (FG)-carbon nanotubes (CNTs)-reinforced micro cylindrical shells. The structure is subjected to harmonic non-uniform temperature distribution and 2D magnetic field. The CNT reinforcement is either uniformly distributed or FG along the thickness direction where the effective properties of nano-composite structure are estimated through Mixture low. The viscoelastic properties of structure are captured based on the Kelvin–Voigt theory. The surrounding viscoelastic medium is considered nonhomogeneous with the spring, orthotropic shear and damper constants. The material properties of cylindrical shell and the viscoelastic medium constants are assumed temperature-dependent. The first order shear deformation theory (FSDT) or Mindlin theory in conjunction with Hamilton\'s principle is utilized for deriving the motion equations where the size effects are considered based on Eringen\'s nonlocal theory. Based on differential quadrature (DQ) and Bolotin methods, the dynamic instability region (DIR) of structure is obtained for different boundary conditions. The effects of different parameters such as volume percent and distribution type of CNTs, mode number, viscoelastic medium type, temperature, boundary conditions, magnetic field, nonlocal parameter and structural damping constant are shown on the DIR of system. Numerical results indicate that the FGX distribution of CNTs is better than other considered cases. In addition, considering structural damping of system reduces the resonance frequency.

Forced vibrations of fluid-conveyed double piezoelectric functionally graded micropipes subjected to moving load

This article is aimed to study the forced vibrations of double piezoelectric functionally graded material micropipes conveying fluid carrying a moving load based on the flexoelectricity theory and modified couple stress theory. The two micropipes are identical and are connected with each other continuously by visco-Pasternak medium. The top micropipe is traversed by a load and is labeled as the primary micropipe. The bottom micropipe is labeled as the secondary micropipe. Non-classical governing equations together with corresponding boundary conditions based on the Hamilton’s principle are obtained and then solved by differential quadrature and Runge–Kutta methods. The influences of the material gradient index, length scale parameter, potential electrical, visco-Pasternak foundation, fluid velocity, various boundary conditions, velocity of the moving load and flexoelectric effect on the dimensionless dynamic deflections of system are discussed. The results show that the flexoelectric and piezoelectric effects tend to increase/decrease the dimensionless dynamic deflections of the primary/secondary pipe, respectively. In addition, the effects of spring constant, shear constant and damping coefficient of the visco-Pasternak medium on the dynamic displacement of the primary and secondary micropipes are vice versa.

Elastic strain response in the modified phase-field-crystal model**Project supported by the National Natural Science foundation of China (Grant Nos. 51571165 and 51371151), Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second phase), China, and the Fundamental Research Funds for the Central Universities, China (Grant No. 3102015BJ(II)ZS001).

To understand and develop new nanostructure materials with specific mechanical properties, a good knowledge of the elastic strain response is mandatory. Here we investigate the linear elasticity response in the modified phase-field-crystal (MPFC) model. The results show that two different propagation modes control the elastic interaction length and time, which determine whether the density waves can propagate or not. By quantitatively calculating the strain field, we find that the strain distribution is indeed extremely uniform in case of elasticity. Further, we present a detailed theoretical analysis for the orientation dependence and temperature dependence of shear modulus. The simulation results show that the shear modulus reveals strong anisotropy and the one-mode analysis provides a good guideline for determining elastic shear constants until the system temperature falls below a certain value.

Buckling analysis of embedded laminated plates with agglomerated CNT-reinforced composite layers using FSDT and DQM

Laminated plates have many applications in different industrials. Buckling analysis of these structures with the nano-scale reinforcement has not investigated yet. However, buckling analysis of embedded laminated plates with nanocomposite layers is studied in this paper. Considering the single-walled carbon nanotubes (SWCNTs) as reinforcement of layers, SWCNTs agglomeration effects and nonlinear analysis using numerical method are the main contributions of this paper. Mori-Tanaka model is applied for obtaining the equivalent material properties of structure and considering agglomeration effects. The elastic medium is simulated by spring and shear constants. Based on first order shear deformation theory (FSDT), the governing equations are derived based on energy method and Hamilton's principle. Differential quadrature method (DQM) is used for calculating the buckling load of system. The effects of different parameters such as the volume percent of SWCNTs, SWCNTs agglomeration, number of layers, orientation angle of layers, elastic medium, boundary conditions and axial mode number of plate on the buckling of the structure are shown. Results indicate that increasing volume percent of SWCNTs increases the buckling load of the plate. Furthermore, considering agglomeration effects decreases the buckling load of system. In addition, it is found that the present results have good agreement with other works.

Comparison of different cylindrical shell theories for stability of nanocomposite piezoelectric separators containing rotating fluid considering structural damping

Rotating fluid induced vibration and instability of embedded piezoelectric nano-composite separators subjected to magnetic and electric fields is the main contribution of present work. The separator is modeled with cylindrical shell element and the structural damping effects are considered by Kelvin–Voigt model. Single-walled carbon nanotubes (SWCNTs) are used as reinforcement and effective material properties are obtained by mixture rule. The perturbation velocity potential in conjunction with the linearized Bernoulli formula is used for describing the rotating fluid motion. The orthotropic surrounding elastic medium is considered by spring, damper and shear constants. The governing equations are derived on the bases of classical shell theory (CST), first order shear deformation theory (FSDT) and sinusoidal shear deformation theory (SSDT). The nonlinear frequency and critical angular fluid velocity are calculated by differential quadrature method (DQM). The detailed parametric study is conducted, focusing on the combined effects of the external voltage, magnetic field, visco-Pasternak foundation, structural damping and volume percent of SWCNTs on the stability of structure. The numerical results are validated with other published works as well as comparing results obtained by three theories. Numerical results indicate that with increasing volume fraction of SWCNTs, the frequency and critical angular fluid velocity are increased.

Buckling of sandwich plates with FG-CNT-reinforced layers resting on orthotropic elastic medium using Reddy plate theory

Present paper deals with the temperature-dependent buckling analysis of sandwich nanocomposite plates resting on elastic medium subjected to magnetic field. The lamina layers are reinforced with carbon nanotubes (CNTs) as uniform and functionally graded (FG). The elastic medium is considered as orthotropic Pasternak foundation with considering the effects of thermal loading on the spring and shear constants of medium. Mixture rule is utilized for obtaining the effective material properties of each layer. Adopting the Reddy shear deformation plate theory, the governing equations are derived based on energy method and Hamilton's principle. The buckling load of the structure is calculated with the Navier's method for the simply supported sandwich nanocomposite plates. Parametric study is conducted on the combined effects of the volume percent and distribution types of the CNTs, temperature change, elastic medium, magnetic field and geometrical parameters of the plates on the buckling load of the sandwich structure. The results show that FGX distribution of the CNTs leads to higher stiffness and consequently higher buckling load. In addition, considering the magnetic field increases the buckling load of the sandwich nanocomposite plate.

Reliability Analysis of Nanocomposite Beams Reinforced with CNTs under Buckling Forces Using the Conjugate HL-RF

In this paper, the nonlinear conjugate map is applied based on the conjugate Hasofer-Lind and Rackwitz- Fiessler (CHL-RF) method to evaluate the reliability index using the first order reliability method of the embedded nanocomposite beam, which is made of a polymer reinforced with carbon nanotubes (CNTs). The structure is simulated with the Timoshenko beam model. The Mori-Tanaka model is applied for calculating the effective material properties of the nanocomposite beam and the surrounding elastic medium is considered as spring and shear constants. The governing equations are derived based on the energy method and the Hamilton's principle. Moreover, using an analytical method, the buckling performance function of the structure is obtained. The effects of the basic random variables including the length-to-thickness ratio of the beam (L/h), the spring constant, and the shear constant of the foundation with respect to the volume fraction of CNTs are investigated based on the reliability index of the nanocomposite beam which is subjected to an axial force of 20 GPa. The results indicate that the failure probabilities of the studied nanocomposite beams are sensitive to the length-to-thickness ratio of the beam (L/h) and the spring constant of the foundation variables.

Differential cubature method for vibration analysis of embedded FG-CNT-reinforced piezoelectric cylindrical shells subjected to uniform and non-uniform temperature distributions

Vibration analysis of embedded functionally graded (FG)-carbon nanotubes (CNT)-reinforced piezoelectric cylindrical shell subjected to uniform and non-uniform temperature distributions are presented. The structure is subjected to an applied voltage in thickness direction which operates in control of vibration behavior of system. The CNT reinforcement is either uniformly distributed or functionally graded (FG) along the thickness direction indicated with FGV, FGO and FGX. Effective properties of nano-composite structure are estimated through Mixture low. The surrounding elastic foundation is simulated with spring and shear constants. The material properties of shell and elastic medium constants are assumed temperature-dependent. The motion equations are derived using Hamilton's principle applying first order shear deformation theory (FSDT). Based on differential cubature (DC) method, the frequency of nano-composite structure is obtained for different boundary conditions. A detailed parametric study is conducted to elucidate the influences of external applied voltage, elastic medium type, temperature distribution type, boundary conditions, volume percent and distribution type of CNT are shown on the frequency of system. In addition, the mode shapes of shell for the first and second modes are presented for different boundary conditions. Numerical results indicate that applying negative voltage yields to higher frequency. In addition, FGX distribution of CNT is better than other considered cases.

Study of phase transformation and elastic properties of ThX (X = N, P, As and Sb) under high-pressure

ABSTRACTAn improved interaction potential model (IIPM) has been formulated to theoretically predict the pressure induced phase transition, elastic properties and thermophysical properties of thorium monopnictides (ThX; X = N, P, As and Sb). The phase transition pressures and volume drop obtained from this model show a better agreement with the available experimental than theoretical results. We have achieved elastic moduli, anisotropy factor, Poisson's ratio, Kleinman parameter, shear and stiffness constants on the basis of the calculated elastic constants. To know the anharmonic properties, we have also computed the third-order elastic constants, first-order pressure derivatives of second-order elastic constants and thermophysical quantities. Our results are in reasonable agreement with available measured and others reported data which supports the validity of model.

First Principles Investigation of Fluorine Based Strontium Series of Perovskites

Density functional theory is used to explore structural, elastic, and mechanical properties of SrLiF3, SrNaF3, SrKF3 and SrRbF3 fluoroperovskite compounds by means of an ab-initio Full Potential-Linearized Augmented Plane Wave (FP-LAPW) method. Several lattice parameters are employed to obtain accurate equilibrium volume (Vo). The resultant quantities include ground state energy, elastic constants, shear modulus, bulk modulus, young's modulus, cauchy's pressure, poisson's ratio, shear constant, ratio of elastic anisotropy factor, kleinman's parameter, melting temperature, and lame's coefficient. The calculated structural parameters via DFT as well as analytical methods are found to be consistent with experimental findings. Chemical bonding is used to investigate corresponding chemical trends which authenticate combination of covalent-ionic behavior. Furthermore electron density plots as well as elastic and mechanical properties are reported for the first time which reveals that fluorine based strontium series of perovskites are mechanically stable and posses weak resistance towards shear deformation as compared to resistance towards unidirectional compression while brittleness and ionic behavior is dominated in them which decreases from SrLiF3 to SrRbF3. Calculated cauchy's pressure, poisson's ratio and B/G ratio also proves ionic nature in these compounds. The present methodology represents an effective and influential approach to calculate the whole set of elastic and mechanical parameters which would support to understand various physical phenomena and empower device engineers for implementing these materials in numerous applications.

Ab initio studies on electronic and magnetic properties of X2PtGa (X=Cr, Mn, Fe, Co) Heusler alloys

Using first-principles calculations based on density functional theory, we probe the electronic and magnetic properties of X2PtGa (X being Cr, Mn, Fe, Co) Heusler alloys. Our calculations predict that all these systems possess inverse Heusler alloy structure in the respective ground states. Application of tetragonal distortion leads to lowering of energy with respect to their cubic phase. The equilibrium volumes of both the phases are nearly the same. These indicate that the materials studied here are prone to undergo martensite transition, as has been recently shown theoretically for Mn2PtGa in the literature. Ground state with a tetragonal symmetry is corroborated by the observation of soft tetragonal shear constants in the cubic phase. By comparing the energies of various types of magnetic configurations we predict that Cr2PtGa and Mn2PtGa possess ferrimagnetic configuration whereas Fe2PtGa and Co2PtGa possess ferromagnetic configuration in their respective ground states.

Surface stress effects on the free vibration and bending analysis of the nonlocal single-layer graphene sheet embedded in an elastic medium using energy method

In this article, using energy method, the effect of surface stress on the free vibration and bending analysis of single-layer graphene sheet embedded in an elastic medium based on nonlocal elasticity theory is studied. Surface stress plays a more important role due to the high surface-to-volume ratio in nanoscale materials. For this purpose, Gurtin–Murdoch continuum mechanics approach is used. The effects of surface properties including surface elasticity, surface residual stresses and surface mass density are considered. In this research, the effects of Winkler spring constant, Pasternak shear constant, aspect ratio, Young’s modulus of surface layer, surface residual stress, nonlocal parameter on the natural frequency ratio and deflection of single-layer graphene sheet are investigated. The results indicate that the natural frequency ratio decreases with an increase in the surface residual stress and vice versa for deflection of nonlocal single-layer graphene sheet. Also, the natural frequency ratio increases with an increase in Young’s modulus of surface layer and vice versa for deflection of nonlocal single-layer graphene sheet. Moreover, the elastic medium causes to stiffen the single-layer graphene sheet. The influence of the small-scale parameter on the natural frequency ratio and deflection of single-layer graphene sheet is more significant for lower values of foundation parameters and vice versa for higher values of foundation parameters.

Probing the possibility of coexistence of martensite transition and half-metallicity in Ni and Co-based full-Heusler alloys: Anab initiocalculation

Using first-principles calculations based on density functional theory, we have studied the mechanical, electronic, and magnetic properties of Heusler alloys, namely, Ni$_{2}BC$ and Co$_{2}BC$ ($B$ = Sc, Ti, V, Cr and Mn as well as Y, Zr, Nb, Mo and Tc; $C$ = Ga and Sn). On the basis of electronic structure (density of states) and mechanical properties (tetragonal shear constant), as well as magnetic interactions (Heisenberg exchange coupling parameters), we probe the properties of these materials in detail. We calculate the formation energy of these alloys in the (face-centered) cubic austenite structure to probe the stability of all these materials. From the energetic point of view, we have studied the possibility of the electronically stable alloys having a tetragonal phase lower in energy compared to the respective cubic phase. A large number of the magnetic alloys is found to have the cubic phase as their ground state. On the other hand, for another class of alloys, the tetragonal phase has been found to have lower energy compared to the cubic phase. Further, we find that the values of tetragonal shear constant show a consistent trend : a high positive value for materials not prone to tetragonal transition and low or negative for others. In the literature, materials, which have been seen to undergo the martensite transition, are found to be metallic in nature. We probe here if there is any Heusler alloy which has a tendency to undergo a tetragonal transition and at the same time possesses a high spin polarization at the Fermi level. From our study, it is found that out of the four materials, which exhibit a martensite phase as their ground state, three of these, namely, Ni$_{2}$MnGa, Ni$_{2}$MoGa and Co$_{2}$NbSn have a metallic nature; on the contrary, Co$_{2}$MoGa exhibits a high spin polarization.