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The primary objective of the present investigation is to elucidate the operative micromechanisms influencing the strain rate sensitivity and activation volume in (FeCrNi)99Si1 and FeMnNi medium-entropy alloys. Room-temperature nanoindentation experiments at different loading rates were performed to study the evolution of the strain rate sensitivity and activation volume in (FeCrNi)99Si1 and FeMnNi medium-entropy alloys. The (FeCrNi)99Si1 samples were subjected to plane strain deformation by rolling at 77 and 300 K to study the effect of temperature on the strain rate sensitivity, while the FeMnNi and (FeCrNi)99Si1 samples were subjected to simple shear deformation by high-pressure torsion at 300 K to examine the effect of strains. Contrary to the well-documented trend observed in fcc metals and alloys, where the strain rate sensitivity typically increases with decreasing grain size, the present study reveals a distinct behavior for the current alloys. Similarly, these alloys are characterized by extremely low activation volumes of a few tens of b3 compared to 100–1000 b3 for conventional fcc metals and alloys in the microcrystalline grain size regime. Unlike conventional fcc metals and alloys, there is an insignificant change in the activation volume of the current high-/medium-entropy alloy (H/MEA) with decreasing grain size from the microcrystalline to nanocrystalline regime. The unique evolution of strain rate sensitivity and activation volume in H/MEAs is explained in terms of the evolution of distinct dislocation structures as well as synergistic operation of additional mechanisms such as twinning, phase transformation from fcc to hcp phases, cluster strengthening, and short-range ordering due to the aperiodic energy landscape existing in MEAs. [ABSTRACT FROM AUTHOR]

This article discusses the development of optically clear adhesives (OCAs) derived from biomass for use in foldable displays. The OCAs are synthesized using eco-friendly visible-light-driven polymerization and possess low modulus and excellent creep and recovery properties, making them suitable for foldable devices. The authors synthesized new monomers from terpenes and combined them with established monomers to formulate OCAs with low glass transition temperature (Tg) and good adhesion properties. The properties of the OCAs were confirmed through rheological analysis, and their potential for enhancing the eco-friendliness of foldable devices was demonstrated. The authors also explored a sustainable visible-light-driven polymerization method for synthesizing the OCAs and found that the properties of the OCAs produced using this method were comparable to those produced using conventional UV methods. The authors concluded that the terpenoid-based acrylates used in their study offer advantageous attributes for eco-friendly foldable electronic devices. [Extracted from the article]

Based on the macroscopic structure control theory, The slate with a significant bedding plane is a composite rock mass composed of rock blocks containing microscopic defects, joint surface closure elements, and shear deformation elements. Considering the coupling damage effect of water erosion and triaxial compressive load on bedding structure plane, the transversely isotropic damage constitutive model of slate under triaxial compressive load is derived with the dip angle of bedding and confining pressure as the variable. Firstly, based on the statistical theory of continuous damage mechanics and the maximum tensile strain criterion, the transversely isotropic deformation constitutive model of rock block with micro-defects is given; Secondly, based on the phenomenological theory of closed deformation and shear-slip deformation mechanism of layered structural plane under the coupling action of water erosion and triaxial compression load, the calculation formula of axial deformation of layered structural plane under the coupling action is given; Finally, to verify the accuracy of the established constitutive model, triaxial compression tests are carried out to study the influence of dip angle and confining pressure on the macroscopic mechanical properties and mechanism of slate. The results show that: the established triaxial compression damage constitutive model of bedding slate can accurately describe the stress–strain relationship of bedding slate after water environment erosion. With the increase of bedding dip angle, the strength and deformation capacity of the bedding slate first decreases and then increases, showing a U-shaped distribution as a whole. There are three main types of failure: tension shear composite failure, shear slip failure, and splitting tension failure. [ABSTRACT FROM AUTHOR]

The authors propose an intelligent computational method using the deep feedforward neural network integrated with an improved balance composite motion optimization algorithm to formulate a so-called iBCMO-DNN for solving the stochastic thermal buckling problems of functionally graded porous microplates. In the present approach, the deterministic behaviors of the functionally graded porous microplates were firstly analyzed by the combination of a unified higher-order shear deformation theory, modified strain gradient theory, and Ritz-type series solutions, and then stochastic responses under uncertainty of material properties are obtained by the iBCMO-DNN algorithm. The deep neural network with the long short-term memory model is used as a surrogate method to replace the time-consuming computational model, while the improved balance composite motion optimization is used to search for the optimal solutions. The obtained numerical results for various boundary conditions, uncertainty parameters, and three types of temperature distribution indicated that the proposed method achieves its accuracy and effectiveness in predicting stochastic thermal buckling of the functionally graded porous microplates. The improved balance composite motion optimization algorithm demonstrates a computational time ∼1.7 times faster than its predecessor. Furthermore, integrating a deep neural network into the improved algorithm reduces computational time to about 2/5 compared to the method without it. [ABSTRACT FROM AUTHOR]

This article investigates the propagation of bending, longitudinal, and shear waves in a smart sandwich nanoplate with a graphene platelet (GPL)-reinforced foam core and magneto-electro-elastic (MEE) surface layers using sinusoidal higher-order shear deformation theory (SHSDT). The suggested nanoplate is comprised of a Ti–6Al–4V foam core placed between MEE surface layers. The MEE surface layers are composed of a volumetric combination of cobalt-ferrite (CoFe2O4) and barium-titanate (BaTiO3). The foam core and MEE face layers' material characteristics are temperature dependent. In this study, three different core types are considered: metallic solid core (Type-I), GPL-reinforced solid core (Type-II) and GPL-reinforced foam core (Type-III), as well as three different foam distributions: symmetrical foam I (S-Foam I), symmetrical foam II (S-Foam II) and uniform foam (U-Foam). To derive the nanoplate's equations of motion and determine the system response, Hamilton's principle and Navier's method are employed. The effects of various parameters such as the wave number, nonlocal parameter, foam void coefficient and distribution pattern, GPL volume fraction, and thermal, electric, and magnetic charges, on the phase velocity and wave frequency are investigated via analytical calculations. The findings of the research indicate that the 3-D wave propagation characteristics of the sandwich nanoplate can be considerably modified or tuned with respect to external loads and material parameters. Thus, the proposed sandwich structure is expected to provide important contributions to radar stealth applications, protection of nanoelectromechanical devices from high frequency and temperature environments, advancement of smart nanoelectromechanical sensors characterized by lightweight and temperature sensitivity and wearable health equipment applications. [ABSTRACT FROM AUTHOR]

In this paper large deformation of the skew microplate made of laminated composite enhanced with graphene nanosheets is investigated using first shear deformation theory (FSDT) when the plate undergoes combination of mechanical and thermal loads. Halpin-Tsai model is utilised to model mechanical properties while for thermal properties Schapery model is considered. First, shear deformation of the plate was obtained while using Green-Lagrange tensor the non-linear strain of the microplate is extracted using the von-Karman assumptions. Then, by Modified Coupled Stress Theory (MCSD), the components of Cauchy and Couple stress tensors are specified. Finally, using Hamilton Principle the governing equation of the microplate and boundary conditions are computed. After deriving analytical governmental equation results are presented for the simple support boundary condition and the proposed model is validated by previously reported data and it proves to be promising. Primary results showed that with raising skew angle deflection and bending moment decreases which means microplate becomes more rigid in higher skew angles. Higher mechanical loads lead to higher deflections and bending moments. Four different configurations of the layers were analysed from which angle-ply configuration possessed highest deflection and bending while UD configuration revealed the lowest values of deflection and bending moment. [ABSTRACT FROM AUTHOR]

Background: For an anisotropic thin-walled tube without changing its circular geometry, only the experimental data of initial yield and subsequent plastic deformation along the axial and circumferential directions can be obtained till now. These experimental data are not sufficient to construct an anisotropic constitutive relation for simulations of tube deformation processes. Objective: A novel shear test of tubular materials is proposed to achieve the state of shearing plastic deformation along the axial direction of thin-walled tubes. Methods: Two semi-circle mandrels and one specially designed tubular specimen are used in the shear experiment. Optimizations of the specimen shape and mandrel structure were carried out by using FE simulation. The influence of the specimen shape, such as the length of the shear zone and the length of the axial slot, on the stress state of the shear zone was discussed. A thin-walled 5052 aluminum tube was used in the shear experiment using the optimized specimen shape. To understand the corresponding relationship between the tensile properties and the shear properties of an anisotropic tube, the uniaxial tension stress-strain relationship was equivalently transformed to the shear stress-stain relationship using the Mises, Tresca, Hill48, and Barlat-lian constitutive functions. Results: After optimizing the specimen shape, the shearing condition of the tested tube is closer to the pure shear stress state. Based on the tests, the pure shear stress state can be maintained to a large deformation extent. The experimental shear stress-strain relationship was compared with the converted stress-strain relationship based on the uniaxial tension tests using the Mises, Tresca, Hill48, and Barlat-lian constitutive functions. The results show a large difference between the transformed stress-strain relationship and the shear stress-strain relationship. Conclusions: This testing method can provide necessary empirical data with the principal stress directions along the direction at an angle of 45° to the tube axis. The shear plastic deformation properties of some anisotropic materials cannot be equivalently described by the experimental data of the tensile test. The shearing characteristics obtained by this novel experimental method can be applied to the characterizations of anisotropic constitutive relations for simulations of tube deformation processes. [ABSTRACT FROM AUTHOR]

This paper presents a novel shear deformation theory for analyzing porous microbeams' bending, buckling, and free vibration resting on a foundation. The proposed shear function incorporating three kinetic variables satisfies zero-traction boundary conditions on the top and bottom surfaces of the beams and does not require a shear correction factor. The modified couple stress theory accounts for the size-dependent effects, and the governing equations are derived from Lagrange's equation using the proposed shear function. Legendre–Ritz functions are developed to analyze the porous microbeams' buckling, free vibration, and bending behaviors. The effects of material length scale parameter, porosity, span-to-height ratio, boundary condition, and foundation parameter on the mechanical responses of beams are investigated. Numerical results demonstrate the accuracy and efficiency of the proposed theory and can serve as benchmarks for future analysis of porous microbeams on elastic foundations. [ABSTRACT FROM AUTHOR]

In the current study, the large deflection of nanobeam according to the modified couple stress theory (MCST) with surface effects (SE) was investigated by applying finite element method (FEM). For modeling of the nanobeam, we applying the Timoshenko beam theory (TBT), and for the solution of the problem, we used a total lagrangian finite element method. Also, shear deformation and axial displacements of nanobeams have been considered in this model. The FEM has been used for the solution of the problem. With the present model, small to large deflection of nanobeam with arbitrary loadings and boundary conditions can be studied. The numerical results for the small deflection of nanobeam achieved by the present model are well matched with results reported in the previous researches. Effects of the ratio of material length scale parameter to thickness on the large deflection of nanobeams have been investigated. Also, the influence of considering different beam constitutive theories in the large deflection analysis of nanobeams has been examined. The results achieved in this study show the relative importance of considering surfaces and size effects in the analysis of nanobeam. [ABSTRACT FROM AUTHOR]

The present study examines a microplate with a porous structure and two nanocomposite piezoelectric layers. All the layers' properties are graded functionally, bonded to each other, and supported by an elastic foundation that can withstand both normal and shear loads. Additionally, carbon nanotubes are used to increase the electro-mechanical performance of the piezoelectric patches, which are exposed to an externally applied electric voltage. Using a higher-order trigonometric shear deformation theory and von Karman's assumptions, the kinematic relations are demonstrated. The governing motion equations are derived using Hamilton's principle and variational technique, and the modified couple stress theory is employed to take the scale effect into account. An analytical method based on Fourier series functions is used to solve the differential motion equations, and the impact of diverse factors such as porosity percentage, pore distribution patterns, carbon nanotubes distribution patterns, and other key parameters on the normalized frequencies of the model is analyzed after verifying the accuracy of the results. The findings of this research may aid in the development and production of smart structures and devices with increased efficiency. [ABSTRACT FROM AUTHOR]

AbstractIn this article, the analytical solution for free oscillation of non-uniform thickness functionally graded porous (FGP) rectangular nanosheets resting on a Pasternak foundation with various boundary conditions (BCs) based on the nonlocal strain gradient theory and surface effect are discovered. The nonlocal stress and strain effects are captured on the nonlocal strain gradient hypothesis, while the surface energy effects are based on the surface elasticity hypothesis. The FGP nanosheet has a nonlinear thickness change in both x and y directions and is placed on the Pasternak elastic foundation. The unique point of this study is to investigate the change of nonlocal and length-scale coefficients along the thickness as mechanical properties of the material. Applying classical shear deformation theory (ignore the effect of shear deformation) combined with Hamilton’s principle, the motion balance equation of non-uniform thickness nanosheets is established. The accuracy of the proposed method is verified through reliable publications. A set of results of natural vibration frequencies of variable thickness FGP nanosheets under the influence of factors are discovered and discussed. The results of this study can be used in design calculations of MEM and NEMs systems in mechanics. [ABSTRACT FROM AUTHOR]

Thermal buckling analysis of a simply supported sandwich cylindrical microshell with piezoelectric layers reinforced with graphene platelets is presented in the current study. The motion equations of the piezoelectric microshell are derived in reference to the first-order shear deformation hypothesis alongside the modified couple stress theory. The critical buckling temperature difference of piezoelectric graphene platelets reinforced cylindrical microshells is derived from adopting Navier's approach and the meshless method. The material properties of every layer for microcomposite shell layers reinforced by graphene platelets are estimated using Halpin–Tsai model. The comparison study is conducted to verify upcoming results. The goal is to investigate the effects of the applied voltage, the thickness of the piezoelectric layers, the distribution pattern, the weight fraction, the material length scale parameter, the length to radius ratio, and the thickness to radius ratio on the buckling of piezoelectric graphene platelets cylindrical microshell. [ABSTRACT FROM AUTHOR]

The present work applies meta-heuristic multi-objective particle swarm optimization (MOPSO) and non-dominated sorting genetic algorithm (NSGA)-II algorithms to predict optimal shape and material distribution of two-directional functionally graded tapered (2DFG-T) microbeams. The cross-section of the microbeam changes linearly along its length in both height and width directions. The rates of these changes are taken as the geometric design variables. Rather than the simple power law, two different trigonometric functions are introduced to provide various effective and flexible 2D- distributions of metal and ceramic phases. Using Hamilton's principle, the mathematical model is derived based on the third order shear deformation theory (TSDT) and modified couple stress theory (MCST). Developing a computationally efficient and time saving semi-analytical approach, the governing set of variable-coefficients partial differential equations is solved for the frequency and critical buckling under different boundary conditions. Several constrained single- and multi-objective optimization problems are formulated and solved to determine optimal material and geometry parameters of 2DFG-T microbeams to achieve maximization of fundamental frequency and/or critical buckling load while minimizing the structural mass. Various optimization results demonstrate that including shape parameters in addition to material distribution parameters as design variables results in more economical and flexible profiles that is critical for the manufacture of 2DFG-T microbeams. The following model can be exploited in the optimum design of FG microscale nanobeams including their shapes and material distribution. [ABSTRACT FROM AUTHOR]

In this study, a thermomechanical rigid-flexible coupling vibration model of the rotating pre-twisted porous functionally graded (PP-FG) thick microplate in a thermal environment is established based on the third-order shear deformation theory (TSDT) and modified couple stress theory (MCST). Three thermal distributions are considered. The effects of temperature and porosity on the equivalent material parameters are accounted for in the modified Voigt rule of mixture. The governing equations of motion are derived using the Euler–Lagrange equation and numerically solved through the complex modal analysis method and the Chebyshev–Ritz method. After validating the convergence and accuracy of the proposed model, the effects of temperature, material length scale parameter (MLSP), rotational speed, porosity index, gradient index, presetting angle, and pre-twist angle on the vibration behavior of microplates were examined. The key findings of the study are as follows: (1) The effects of rotational speed on in-plane and out-of-plane frequencies are opposite. Temperature elevation weakens the size effect and centrifugal stiffening effect on the frequencies. (2) The effects of the porosity index on the frequencies are the opposite when the gradient index exceeds a specific critical value. (3) The effects of the presetting angle on the frequencies are periodic and symmetrical at about 0. The frequencies reach an extreme value when the pre-twist angle is approximately 2π/3 for the cantilever microplate. The proposed model is more sophisticated and comprehensive than others reported in the literature. It offers a more thorough analysis and insight into the behavior and performance of micro-electro-mechanical systems (MEMS) and micro air vehicles (MAVs), particularly when operating in challenging conditions. [ABSTRACT FROM AUTHOR]

AbstractGraphene is highly regarded as a promising material for various engineering purposes due to its remarkable physical characteristics. However, existing higher-order shear deformation theories may struggle to accurately capture the interlaminar mechanical response of functionally graded graphene nanoplatelets (FG-GNP) reinforced composite beams subjected to thermal loads. This arises from the pronounced discrepancies in material properties and thermal expansion coefficients among the various layers, making the interlaminar mechanical behavior of composite structures exceedingly complex under thermal loading. As a result, a meticulous analysis of interlaminar stresses becomes necessary for the structural assessment of GNP-reinforced composite beams under temperature variations. To overcome this limitation, we propose an advanced model incorporating transverse normal thermal deformation, tailored specifically for FG-GNP reinforced composite beams subjected to thermal loads. The developed model primarily boasts two advantages. Firstly, although transverse normal deformation is introduced into the displacement field, no additional displacement variables are increased, thereby maintaining model simplicity and efficiency. Secondly, the model achieves a high-precision interlaminar shear stress field taking into account the interlaminar continuity conditions and temperature effects. Furthermore, the elimination of second-order derivatives of in-plane displacement parameters from the transverse shear stress components leads to a simplification in the finite element implementation. Based on the proposed model, a simple three-node beam element is constructed. The 3D elasticity solutions and the results from alternative modeling frameworks are used to assess the performance of the developed model. Additionally, a comprehensive investigation is conducted to explore the effects of various parameters on the deformations and stresses of GNP-reinforced composite beams. [ABSTRACT FROM AUTHOR]

In the current paper, size‐dependent mechanical analysis of functionally graded porous (FGP) nanobeams resting on Pasternak foundation in thermal environment is presented based on nonlocal strain gradient theory and Gurtin‐Murdoch surface elasticity theory. The nanobeam is modeled based on Euler‐Bernoulli beam theory, Timoshenko beam theory and Reddy's third‐order shear deformation theory and the set of the governing equations are solved for a clamped‐clamped FGP nanobeam using generalized differential quadrature method. Numerical results show that as porosity parameter increases, static deflection increases and critical buckling load decreases, but its effect on the fundamental frequency strongly depends on the porosity distribution pattern. It was revealed that among all studied porosity distribution patterns, the minimum value of the static deflection and maximum values of critical buckling load and fundamental frequency can be achieved using symmetric distribution pattern of pores. It is concluded that tensional residual stress reduces static deflection and increases both critical buckling load and fundamental frequency and temperature rise has reverse effects. [ABSTRACT FROM AUTHOR]

This research focuses on examining the vibrational properties of intelligent curved microbeams (CMBs) that incorporate metal foams and are enhanced with carbon nanotubes-reinforced piezoelectric (CNTRP) actuators. An advanced four-variable theory for shear and normal deformation is applied in the polar coordinate framework to investigate the microstructure, thereby negating the need for a shear correction factor. Additionally, the modified couple stress theory (MCST) is utilized to account for scale effects. The structural attributes exhibit thickness-dependent alterations following predefined functions. The governing equations of motion are deduced using Hamilton’s principle. In instances where the structure has simply supported ends, Fourier series functions are utilized to solve these equations. The outcomes are cross-validated in contradiction with previously documented works with more straightforward setups. The inquiry investigates the effects of critical parameters on the vibrational response of the structure. The results are corroborated in simpler scenarios using existing data in the literature to ensure accuracy. [ABSTRACT FROM AUTHOR]

This article uses the semi-analytical approach to study the combined nonlinear vibration and nonlinear response of a damped porous microplate under nonuniform periodic parametric excitation to understand the complete nonlinear dynamic behavior of the plate. The plate is supported by a Winkler-Pasternak elastic foundation and modeled using modified strain gradient and third-order shear deformation theories to simulate the small-scale effects and shear deformation, respectively. Using Hamilton's principle, the governing partial differential equations of motion are derived and solved using Galerkin's method to convert them into ordinary differential equations (ODEs). These ODEs are solved using a combined incremental harmonic balance (IHB) and arc-length continuation approaches to get the nonlinear vibration (frequency–amplitude curves). The same ODEs are solved using the Newmark-β technique to obtain the nonlinear response (time–amplitude curves). The effect of elastic foundation parameters and aspect ratio on mode shape is presented. The effect of parameters such as the porosity coefficient, type of porosity, Winkler-Pasternak elastic foundation parameters, different size-dependent theories, plate thickness, size of plate, damping coefficient, different loading profiles, and loading concentrations on the nonlinear vibration and nonlinear response is examined. Also, the dependence of initial displacements on the frequency–amplitude curves with respect to the excitation frequency is demonstrated with the help of time-amplitude curves. [ABSTRACT FROM AUTHOR]

In this article, we use a macro-mesoscopic method to analyze the forced vibration behavior of the SiCf/Ti cantilever beam. The shear-lag model was applied to determine the stress-strain relationship of SiCf/Ti composites with matrix cracking, interface debonding, wear, and failure damages under tension-compression loading. We established the cyclic tension-compression constitutive model of SiCf/Ti composites by considering the evolution laws followed by three injury patterns. From a macroscopic perspective, we use the cyclic tension-compression constitutive model to obtain the stiffness reduction at different stress levels and reduce the stiffness at different stress levels. Finally, we use Ansys software to reveal the forced vibration properties of the SiCf/Ti cantilever beam under different acceleration amplitudes. [ABSTRACT FROM AUTHOR]

This study presents a warping included mixed finite element formulation for the static and stress analyses of functionally graded (FG) exact curved beams. Another distinctive feature of this study is to present the range of geometric and material parameters where the first-order shear deformation theory lacks necessary precision. The constitutive equations are derived from the 3D elasticity theory of an elastic continuum. The couple effects are considered in addition to the variations of FG material constituents through the transverse/axial directions. The mixed finite element formulation is enhanced by the cross-sectional warping deformations over a displacement-type finite element formulation. The two-noded curved mixed finite elements with 12 degrees of freedom at per node are derived over exact curvature and length. Satisfactory results are obtained for the static responses and stresses of axially FG-sandwich and transversely FG exact curved beams with power-law dependence compared to the 3D behavior of brick finite elements. Finally, the influences of ellipticity, width to thickness ratio, FG material constituents, and material gradient index on the static response of FG exact curved beams are investigated. [ABSTRACT FROM AUTHOR]

Tantalum, in its most stable Ta 2 O 5 oxide form, has long been recognized as a superior coating material in orthopedic applications. In this study, the ideal mechanical strengths of I41/amd, Cmmm, C2/c, Pm, and Pbam phases of Ta 2 O 5 are investigated from first-principles calculation, where the stress–strain curves under various deformation strains are obtained and the structural evolution in terms of atomic bonding is analyzed. The results reveal that these stable Ta 2 O 5 polymorphs show unusual mechanical strengths on their high symmetric crystalline planes. Shear super-plasticity is found on the (001) crystalline plane of the I41/amd phase in any shear direction. Shear strain-stiffening exists on the (100) crystalline plane of the Pm phase in the shear direction within an angle of ± 18 ° along the [001] direction. Both shear super-plasticity and shear strain-stiffening make these crystalline planes be able to sustain excessively large shear deformations. Large and isotropic shear strengths are predicted on the (010) crystalline planes of Pm and Pbam phases with nearly identical maximum and minimum peak shear stresses approaching 15 GPa. Much stronger compression and tensile strengths are obtained normal to the (010) crystalline plane of the C2/c phase due to its special spring-like bonding structure, which can endure the compression deformation up to 30%. These findings provide guidance for selecting suitable phases of Ta 2 O 5 and growth directions with crystalline planes possessing excellent mechanical properties in applications of Ta 2 O 5 as a coating material on Ti alloys for biomedical replacements of damaged human organs, such as hip joints, dental implants, and artificial hearts. [ABSTRACT FROM AUTHOR]

The present investigation has analyzed the buckling of bi-directional functionally graded conical micro-shells bearing axial loading. The dominant equations serve on the basis of the theory of first-order shear deformation in the modified couple stress theory (MCST). The Ritz technique is used so as to solve the governing equations. Bi-directional functionally graded material is the material used to construct the shell, and in a predefined composition profile, the volume fractions pertaining to the constituent materials constantly vary through the conical edge directions and thickness. The model predictions are compared and successfully validated using the ones available in the literature. According to the results, in comparison with the classical theory, the micro-shell buckling load is higher in the MCST. In addition, the contribution of a number of geometrical and mechanical parameters, for example, radius-to-thickness ratio, thickness-to-length scale ratio, length-to-radius ratio, semi-vertex angle, homogenization schemes, and material gradient indexes, to the buckling performance of conical micro-shells has been investigated. It is noteworthy that this investigation is the first effort to present a buckling analysis for the purpose of bi-directional functionally graded truncated conical micro-shells in accordance with the MCST. [ABSTRACT FROM AUTHOR]

In the present study, the sound transmission loss (STL) through the air-filled rectangular double-walled cross-ply fiber metal laminated (FML) nanoplates under simply supported and clamped boundary conditions is studied using the nonlocal strain gradient theory (NSGT) and third-order shear deformation theory (TSDT). NSGT is complemented with hardening and softening material effects, which can significantly enhance the accuracy of small-scale results. The sound velocity potential and Hamilton's principle are employed to derive the coupled size-dependent vibroacoustic equations. The Galerkin method is exploited to solve vibroacoustic equations and obtain the STL. The developed solution is examined in terms of its accuracy and precision via a comparison with other available data in existing research. The effects of different parameters such as boundary conditions, nonlocal and strain gradient parameters, lay-ups, incident angles, and acoustic cavity depth on the STL through the double-walled FML nanoplates are investigated. [ABSTRACT FROM AUTHOR]

A porous microplate embedded with two nanocomposite piezoelectric layers is investigated in the current work. All three layers are functionally graded and completely attached to each other, and the microstructure lies on a bi-parameter elastic foundation that withstands shear and normal forces simultaneously. Also, an external voltage is subjected to the piezoelectric patches. The mentioned patches are reinforced with carbon nanotubes to enhance their electro-mechanical performance. A higher-order shear deformation theory and von Karman's assumptions are hired to demonstrate the kinematic relations. Next, applying Hamilton's principle and variational technique, the governing motion equations are derived with the help of the modified couple stress theory to capture the scale influence. To solve the system of differential equations, a closed-form Navier method is employed, and by ensuring the correctness of the results, then it turns to investigate the impact of different factors including porosity percentage and also pores' distribution patterns, nanotubes dispersion patterns, and other important factors on the natural frequencies of the model. Obtained results show that symmetric and uniform porosity distributions have the maximum and minimum amounts of natural frequencies. Moreover, the maximum difference between natural frequencies of three different porosity distribution occurs in e0 = 0.95 and is approximately 32%. The current study results may consider to design and produce smart structures and devices with improved performance. [ABSTRACT FROM AUTHOR]

A three-dimensional (3D) thermomechanical vibration model is developed for rotating pre-twisted functionally graded (FG) microbeams according to the refined shear deformation theory (RSDT) and the modified couple stress theory (MCST). The material properties are assumed to follow a power-law distribution along the chordwise direction. The model introduces one axial stretching variable and four transverse deflection variables including two pure bending components and two pure shear ones. The complex modal analysis and assumed mode methods are used to solve the governing equations of motion under different boundary conditions (BCs). Several examples are presented to verify the effectiveness of the developed model. By coupling the slenderness ratio, gradient index, rotation speed, and size effect with the pre-twisted angle, the effects of these factors on the thermomechanical vibration of the microbeam with different BCs are investigated. It is found that with the increase in the pre-twisted angle, the critical slenderness ratio and gradient index corresponding to the thermal instability of the microbeam increase, while the critical material length scale parameter (MLSP) and rotation speed decrease. The sensitivity of the fundamental frequency to temperature increases with the increasing slenderness ratio and gradient index, and decreases with the other increasing parameters. Moreover, the size effect can suppress the dynamic stiffening effect and enhance the Coriolis effect. Finally, the mode transition is quantitatively demonstrated by a modal assurance criterion (MAC). [ABSTRACT FROM AUTHOR]

Glulam timber structural linear elements often show low span-to-depth ratios. Moreover, timber is intrinsically orthotropic with very low shear moduli. These two circumstances justify the substantial contribution of shear strain to the overall deformation of linear elements. Since design specifications for timber beams commonly adopt 1D models, two such elastic models are proposed in this paper for static plane behavior, where, instead of fully orthotropic, glulam is assumed to be transversely isotropic. These models provide a good compromise between accuracy and simplicity for design proposes. A 3-field mixed formulation is generalized in order to produce two new 1D finite elements suitable for modeling transversely isotropic elastic glulam beams. To assess the accuracy of these new finite elements the results they produce are compared with those determined with a plane stress transversely isotropic 2D finite element. The included examples show that the proposed combination of transverse isotropy with a third order shear deformation model provides a suitable background to the 1D modeling of glulam beams with improved accuracy when compared to the models conventionally used in design. The paper is concluded with a parametric analysis which identifies the cases where the improved models should be used instead of simpler ones. [ABSTRACT FROM AUTHOR]

Featured Application: The failure analysis of soil in the field of geotechnical engineering. The localization of deformation in shear bands is a fundamental phenomenon in granular materials like soil. In this study, we focus on the characteristics of shear bands, particularly the size effect, by implementing biaxial discrete element method (DEM) modeling. Firstly, we describe the establishment of the biaxial experimental model with dense sands. Then, we implement analyses of specimens with different sizes and find that there is a clear size effect in the stress–strain curve after the peak strength point, and there is less of a size effect in the angle of the shear band; the angle is consistent with Arthur's theory. Finally, the reason for the size effect is analyzed using the width of the shear band and the porosity inside the shear band. As the specimen size increases, the ratio between the shear band area and the whole specimen decreases. This effect reduces as the isotropic confining stress increases. The difference in the proportion of the shear band area mainly causes the size effect that affects the specimen deformation characteristics. We also find that with the increase in isotropic confining stress, the type of shear band gradually changes from cross-type to single-type. Our study provides valuable insights into understanding the behavior of granular materials. [ABSTRACT FROM AUTHOR]

Present study deals with the nonlinear analysis of thermally induced deflection and snap-through buckling in functionally graded porous (FGP) curved nanotubes. It is assumed that the curved nanotube is rested on a two-parameter nonlinear elastic foundation. The curved nanotube is subjected to uniformly distributed transverse pressure loading and also uniform temperature rise. Distribution of thermomechanical properties in the thickness of curved nanotubes is radially graded according to a power law function. The even type of porosity distribution patterns is included into the formulation and all properties are considered as temperature dependent. The nonlocal strain gradient and uncoupled thermoelasticity theories are provided to analyze the geometrically nonlinear behaviors of curved nanotubes. The equilibrium equations are obtained based on the high-order shear deformation theory. To capture the large deformations, the von Kármán type of nonlinear kinematic assumptions is included. Two types of immovable boundary conditions are considered which are simply-supported and clamped-clamped. The equilibrium equations are reformulated and transferred into the dimensionless presentation. The closed-form expressions are provided to trace the thermal/mechanical load-deflection paths of curved nanotubes using the two-step perturbation technique. Numerical results of this study are compared with the available data in the literature for the macro-scale curved tubes. After that novel parametric results are provided to discuss the effects of nonlocal and length scale parameters, boundary conditions, porosity coefficient, foundation stiffness, power law exponent, and geometrical parameters. [ABSTRACT FROM AUTHOR]

In this article, a size-dependent analysis is conducted for the geometrically nonlinear transient vibration of a porous microplate in the presence of nonlocal and modified stress tensors, solved by the isogeometric analysis (IGA) method. Pursuing the primary objective, the effective characteristics of porous graphene platelet material (GPL) from uniform and non-uniform porosity distributions are estimated by utilizing the Halpin–Tsai model. The governing equations and the integrated nonlocal modified couple stress theory for nonlinear transient vibration are derived based on uniform rational B-spline. Furthermore, the efficient discretization technique is capable of meeting C1 continuity requirements. It is demonstrated that the theory, introducing a combination of two tensors into the higher-order shear deformation theory, can accurately capture the size effects on the transient dynamic responses. The magnitude of transient displacements is diminished, and the ability of the nano-/microplate to withstand impulse loads increases as the pores concentrate on the center of the neutral axis regarding the non-uniform porosity distribution. The enhancement of the nonlinear transient responses is attributed to the increase in modified couple stress, which generates greater structural rigidity than that reduced by nonlocality. Finally, the new assessment results are detailed by analyzing the size-dependent parameter, nonlocal variation, porosity coefficient, and the different porosity distribution schemes that aim to decide the responses of the GPLs' microstructure. [ABSTRACT FROM AUTHOR]

Displacement mode has a significant influence on the distribution and magnitude of lateral earth pressures and the failure mechanisms of retaining walls. This study performed five model tests to evaluate the responses of coarse sand-backfilled retaining walls under five displacement modes including uniform translation (UT), rotation around the base (RB), rotation around the top (RT), counter-clockwise rotation around the midpoint (RM-CC), and clockwise rotation around the midpoint (RM-C). The measured lateral earth pressures behind each wall were compared with the calculated values using the analytical solutions from the literature. The failure mechanisms of the retaining walls under different displacement modes were evaluated in terms of their backfill deformation and shear strain contours. Test results show that the measured lateral earth pressures at rest and limit equilibrium (LE) had nonlinear distributions, and the RM-C mode resulted in the largest LE earth pressures as compared with the other four modes. The comparisons show that the measured at-rest and LE earth pressures were in good agreement with those calculated by Jaky's method and Harrop-Williams' method, respectively. For the retaining walls under the UT, RB, and RT modes, the required wall movement to reach the LE state was approximately 0.4%H where H is the height of the retaining wall. For the retaining walls under the RM-CC and RM-C modes, the required wall movements above the rotation point and below the rotation point to reach the limit equilibrium were 0.4%H and 0.2%H, respectively. The backfill behind the wall under the RB or RM-C mode showed progressive failure, while the backfill under the UT, RT, or RM-CC mode showed quick failure. [ABSTRACT FROM AUTHOR]

The aim of this research is to investigate the frequency of conical-shaped shells, consisting of different materials, based on higher-order shear deformation theory (HSDT). The shells are of non-uniform thickness, consisting of two to six symmetric cross-ply layers. Simply supported boundary conditions were used to analyse the frequency of conical-shaped shells. The differential equations, consisting of displacement and rotational functions, were approximated using spline approximation. A generalised eigenvalue problem was obtained and solved numerically for an eigenfrequency parameter and associated eigenvector of spline coefficients. The frequency of shells was analysed by varying the geometric parameters such as length of shell, cone angle, node number in circumference direction and number of layers, as well as three thickness variations such as linear, sinusoidal and exponential. It was also evident that by varying geometrical parameters, the mechanical parameters such as stress, moment and shear resultants were affected. Research results concluded that for three different thickness variations, as the number of layers of conical shells increases, the frequency values decrease. Moreover, by varying length ratios and cone angles, shells with variable thickness had lower frequency values compared to shells of constant thickness. The numerical results obtained were verified through the already existing literature. It is evident that the present results are very close to the already existing literature. [ABSTRACT FROM AUTHOR]

We study the flexoelectric effect induced in an infinite strip of a dielectric material, due to an applied shear deformation at the upper surface, while the lower surface is fixed. The model incorporates dynamic spontaneous polarization, flexocoupling deformation, and microinertia effects to evaluate these effects combined. The variation of the Hamiltonian functional in the medium, and of the external forces yields the governing equations and the boundary conditions. There are many types of applied boundary conditions besides the initial conditions, where the initial conditions are imposed due to the dynamics of many effects in the mathematical modelling formulation. In addition to that, the boundary conditions are divided into two groups, where the first group contains mechanical boundary conditions such as traction boundary conditions and displacement boundary conditions for the classical treatment as in the theory of elasticity while for the strain gradient theory of elasticity, conditions for higher-order traction vector should be imposed and cannot be neglected. The proposed technique depends on applying Laplace’s transform to the field equations to obtain the characteristic equation, the roots of which are expressed in terms of the s;-transform parameter and other parameters related to the elastic and electric properties of the material. Those roots which produce a bounded solution are then approximated using Taylor’s expansion, then the boundary conditions are applied to complete the solution. This technique enables to obtain the solution in terms of simple analytical functions that are easily inverted from the s-domain to the time domain. This technique is applied to a simple shear deformation problem to study the dynamical flexoelectric effect in dielectric materials due to shear displacement and external electric potential. A suitable material, such as Strontium Titanate material, SrTiO3, is used for numerical simulation, and the results are analyzed, discussed, and represented graphically. [ABSTRACT FROM AUTHOR]

This article explores the phenomenon of adiabatic shear bands (ASB) in materials under dynamic loading. It discusses the initiation and growth of ASB, as well as the influence of initial defects and thermoplastic instability. The study uses statistical theory and self-similar solutions to understand the behavior of microshears and the scaling properties of shear bands. The findings contribute to a better understanding of ASB phenomena and their impact on material properties. The article includes experimental analysis and numerical simulations to support its conclusions. [Extracted from the article]

The paleo-tectonic stress field was hereby inverted by using the stereographic projection method through field and underground observations of conjugate shear joints. On the basis of analyzing and studying the characteristics of gas occurrence in mining areas, the control effect of paleo-tectonic stress field on gas occurrence was discussed from three aspects of gas generation, preservation environment and gas migration. The results show that: (1) During the Indosinian and early-middle Yanshan period, the coal seam was buried deep, and the temperature and pressure conditions were suitable for massive gas generation, especially during the Indosinian period featuring massive gas generation and weak gas migration; (2) During the late Yanshan period, the metamorphic evolution rate of coal seams accelerated, secondary hydrocarbon generation occurred in the coal seams, and a large amount of gas was generated. Meanwhile, the gas migration was enhanced. The gas generation amount was much larger than the emission amount, therefore, making it still a period of massive gas generation in general; (3) During the Himalayan period, the coal measure stratum was in the uplift stage, and a large number of geological structures were developed in the stratum. The tectonic stress field in this period caused the escape of massive coal seam gas. Multi-stage tectonic stress field acted on coal measures strata in turn, resulting in gas generation in coal seam and gas migration at the same time. Besides, gas occurrence is the superposition effect of gas generation, preservation conditions, and gas migration in coal seam. [ABSTRACT FROM AUTHOR]

Purpose: Flexoelectricity refers to the phenomenon of the link between electrical polarization and strain gradient fields in piezoelectric materials, particularly at the nanoscale. The goal of this study is to look into the bending and vibration properties of piezoelectric sandwich nanoplates in more detail, focusing on the flexoelectric effect and nonlocal strain gradient. Method: The plate consists of three distinct layers, including two outside skin layers formed of piezoelectric smart material exhibiting the flexoelectric effect and an inner core layer consisting of functionally graded porous (FGP) material. The general equations of motion with improved accuracy are derived using Hamilton's principle and the revised higher order shear deformation plate theory (RPT). The use of the Galerkin–Vlasov method allows for the determination of the static bending characteristics and particular vibration frequencies of plates with various boundary conditions. A computational program is implemented using the Matlab software platform. Then, the program's correctness is assessed by doing a comparative analysis using previously published, dependable findings in specific instances of the model described in the article. Moreover, it is crucial to carry out a comprehensive analysis to evaluate the influence of various attributes on a system's static bending response and free vibration. The parameters include the flexoelectric effect, nonlocal and strain gradient parameters, elastic foundation stiffness coefficient, porosity coefficient, and geometric conditions. Results: The results of this research have practical consequences for the effective planning and management of similar systems, such as micro-electro-mechanical and nano-electromechanical devices. The results of this work are an important premise for developing more complex problems shortly, such as buckling analysis and dynamics problems. In addition, this is also a valuable reference for engineers designing models in engineering practice. Conclusion: The article presents a set of numerical experiments that provide significant findings. The stiffness of the plate is increased by the parameter f14, and therefore, the maximum deflection decreases as f14 rises. Nonlocal and strain gradient coefficients have contrary effects on the structure, so modulating these two coefficients is crucial for regulating the structure's stiffness. The ratio between the thicknesses of the piezoelectric layer and the FGP core layer plays a crucial role in the study of increasing or decreasing the overall structure's stiffness. An augmentation in the grading index will lead to a decrease in the overall stiffness of the structure, while an augmentation in the elastic base stiffness would result in an increase in the overall stiffness. Furthermore, the porosity coefficient, contingent upon the characteristics of the object, will induce either an augmentation or diminution in the magnitude of the inherent vibration frequency. However, it is quite probable that the displacement value of the plate will be augmented. Some new points in the article: The plate is composed of three layers with two skin layers made of piezoelectric smart material with flexoelectric effect and a core layer made of functionally graded porous material. The nonlocal and strain gradient coefficients change along the thickness direction and the porosity. Navier and Galerkin–Vlasov analytical methods are applied with many different boundary conditions. [ABSTRACT FROM AUTHOR]

A major challenge in simulating glassy systems is the ability to generate configurations that may be found in equilibrium at sufficiently low temperatures, in order to probe static and dynamic behavior close to the glass transition. A variety of approaches have recently explored ways of surmounting this obstacle. Here, we explore the possibility of employing mechanical agitation, in the form of cyclic shear deformation, to generate low energy configurations in a model glass former. We perform shear deformation simulations over a range of temperatures, shear rates, and strain amplitudes. We find that shear deformation induces faster relaxation toward low energy configurations, or overaging, in simulations at sufficiently low temperatures, consistently with previous results for athermal shear. However, for temperatures at which simulations can be run until a steady state is reached with or without shear deformation, we find that the inclusion of shear deformation does not result in any speed up of the relaxation toward low energy configurations. Although we find the configurations from shear simulations to have properties indistinguishable from an equilibrium ensemble, the cyclic shear procedure does not guarantee that we generate an equilibrium ensemble at a desired temperature. In order to ensure equilibrium sampling, we develop a hybrid Monte Carlo algorithm that employs cyclic shear as a trial generation step and has acceptance probabilities that depend not only on the change in internal energy but also on the heat dissipated (equivalently, work done). We show that such an algorithm, indeed, generates an equilibrium ensemble. [ABSTRACT FROM AUTHOR]

A study is carried out on free vibration characteristics of a composite laminated plate under non-uniform gradient temperature distribution along the thickness (NGTDT). The NGTDT will cause different thermal stress and deformation compared with no gradient or uniform gradient temperature distribution along the thickness. The governing equation is established considering the influence of NGTDT using the von Karman–type geometric nonlinearity and the first-order shear deformation theory based on Hamilton's principle. The semi-analysis solution is solved by an iteration method, and it is in good agreement with the results of FEM. The solutions show that the NGTDT leads to the critical buckling temperature of the plate that is no longer constant but varies with different NGTDT, that is, the transition point of the resonant frequency decreasing first and then increasing with the temperature is related to the NGTDT. This is very different from the results caused by no gradient or uniform gradient temperature distribution along the thickness. [ABSTRACT FROM AUTHOR]

As a result of conventional wire-forming processes, the residual stress distribution in wires is frequently unfavorable for subsequent forming processes such as bending operations. High tensile residual stresses typically occur in the near-surface region of the wires and can limit further application and processability of the semi-finished products. This paper presents an approach for tailoring the residual stress distribution by modifying the forming process, especially with regard to the die geometry and the influence of the drawing velocity as well as the wire temperature. The aim is to mitigate the near-surface tensile residual stresses induced by the drawing process. Preliminary studies have shown that modifications in the forming zone of the dies have a significant impact on the plastic strain and deformation direction, and the approach can be applied to effectively reduce the process-induced near-surface residual stress distributions without affecting the diameter of the product geometry. In this first approach, the process variant using three different drawing die geometries was established for the metastable austenitic stainless steel X5CrNi18-10 (1.4301) using slow (20 mm/s) and fast (2000 mm/s) drawing velocities. The residual stress depth distributions were determined by means of incremental hole drilling. Complementary X-ray stress analysis was carried out to analyze the phase-specific residual stresses since strain-induced martensitic transformations occurred close to the surface as a consequence of the shear deformation and the frictional loading. This paper describes the setup of the drawing tools as well as the results of the experimental tests. [ABSTRACT FROM AUTHOR]

In this research paper a refined shear and deformation theory for buckling of functionally graded FGM plates under mechanical loading is presented. The shear stress variation through the thickness in a parabolic form is accounted for in this theory, and satisfies the condition of the transversal shear stress null on the upper and bottom edges of the plate without using shear correction coefficients. Unlike the conventional other shear stress and deformation theories, only four unknowns involved in the proposed refined theory, which has many resemblances to traditional plate theory. boundary conditions, equilibrium equations and stress expressions. The properties of the functionally graded plate are varying following a power law distribution of the fraction’s volume of the constituents. Equilibrium equations are derived from the virtual works principle. The solution of simply supported functionally graded plates is deduced and their results are compared against those of first-order theory and higher-order theories. It can be said that the suggested theory is effective and accurate in determining the buckling behavior of FGM plates. [ABSTRACT FROM AUTHOR]

Purpose: This article presents a Legendre-Ritz solution for free vibration and buckling analysis of porous microbeams. Background and Method: The beam model is based on the modified couple stress theory and higher-order shear deformation theory. Three porosity distributions of the beam, including uniform, symmetric, and asymmetric porosity distribution, are considered. The equation of motion is established from Lagrange's equation. The Legendre polynomial, which possesses the orthonormal and recursion properties, is developed to approximate the displacement field, and the Ritz procedure is used to find the porous microbeam's natural frequency and critical buckling load. Result: Numerical examples are conducted to assess the present method's efficiency and investigate the effect of the material length scale parameter, boundary condition, and porosity ratio on porous microbeams' frequency and critical buckling load. Conclusion: The study indicates that the Legendre-Ritz solution is simple and effective for analyzing porous microbeams' vibration and buckling behaviors. [ABSTRACT FROM AUTHOR]

In this paper, free vibration analysis and temperature-dependent buckling behavior of porous functionally graded magneto-electro-thermo-elastic material consisting of cobalt ferrite and barium titanate were modeled and analyzed. A high-order sinusoidal shear deformation theory was used to accurately model the anisotropic material behavior. The study examined the porosity role variation across thickness in the buckling and free vibration behavior of nanobeams, as well as the effects of magneto-electro-elastic coupling, thermal stresses, nonlocal properties, externally applied electric and magnetic field potential, and porosity volume fraction. [ABSTRACT FROM AUTHOR]

A static package design of a functionally graded porous plate in microscale which is coated by two polymeric piezoelectric carbon nanotubes reinforced composite (CNTRC) face sheets is provided in this study. The microstructure rests on the Pasternak foundation and is subjected to thermal load. Furthermore, face sheets are subjected to the electric field. With the aid of a quasi-3D hyperbolic shear deformation theory, governing equations of the microplate are derived and then its critical buckling loads are calculated. The properties of all layers alter continuously along with thickness direction due to the CNTs and pores distributions. The size effects are captured by the means of modified couple stress theory (MCST). By conducting the current study, the results emerged in detail to assess the effects of different parameters on buckling of structure. For instance, it is revealed that the highest and lowest critical buckling load and consequently stiffness, is due to the V–A and A–V CNTs dispersion type, respectively. Furthermore, it is revealed that by porosity coefficient enhancement, critical buckling load and consequently, stiffness are reduced dramatically. Current paper outcomes can be used in different fields of sciences such as optimum design of engineering structures or various high-tech industries as aerospace factories. [ABSTRACT FROM AUTHOR]

This work aims to develop a size-dependent mathematical model to analyze the nonclassical size-dependent vibration response of viscoelastic perforated higher-order nanobeams (VEPHONBs) embedded in an elastic foundation and subjected to dynamic moving loads. The nonclassical strain gradient theory is adopted to capture the microstructure as well as the size length-scales effects. The Kelvin–Voigt viscoelastic material model is utilized to simulate the internal material damping. Regular square perforation pattern is considered. Shear deformation effect due to cutouts is incorporated by adopting the higher-order shear deformation beam theory. The moving load is portrayed by point load and harmonic type. The Hamilton approach is applied to derive the dynamic equations of motion considering viscoelasticity as well as size dependency effects. Based on the Navier and Newmark techniques, a mixed analytical–numerical solution is developed and verified by comparing the obtained results with the available results in the literature. Parametric studies are conducted to show the influence of the different design parameters on the transient vibration behavior of viscoelastic perforated higher-order nanobeams under moving load. The proposed procedure is supportive in the analysis and design of perforated viscoelastic NEMS structures under moving load. [ABSTRACT FROM AUTHOR]

Based on the proposed numerical model of the stress-strain state of polymineral rocks, which describes the formation of blastomylonites in the Yenisei Regional Shear Zone (YRSZ) in the Yenisei Ridge, the possibility of local tectonic overpressure exceeding the lithostatic pressure in rocks subjected to shear deformations is shown. For tectonites of the southern (Angara–Kan block) and northern (Isakovka terrane and Garevka complex) segments of the YRSZ, estimates of the maximum overpressure were obtained from 2–3 to 4–5 kbar, which range from 25 to 50% of the lithostatic pressure. It is shown that the excess pressures can be preserved in a local volume on a geological time scale sufficient for their fixation in metamorphic minerals. Model values of overlithostatic pressure in the garnet–amphibole tectonites and geobarometric estimates of peak values during stress metamorphism allow us to offer new evidence for pressure inhomogeneity in natural mineral associations. Using the results of numerical modeling for the evolution of metabasite blastomylonites, it was established that the overpressure at the stage of syn-deformation metamorphism in the shear zone is possible at temperatures up to 600–650°C and not reaching 800°C; the presence of fluid or partial melt prevents the occurrence of overpressure. Magnitudes of excess pressure caused by shear stresses depend on the mineral composition and structure of the rock. [ABSTRACT FROM AUTHOR]

A new quasi-3D finite element model is formulated and implemented in this research to evaluate the free vibration and stability behaviors of thick functionally graded (FG) beams. The current model is founded on an accurate shear and normal deformation beam theory. The traction-free boundary conditions are guaranteed with no shear correction factors by employing the hyperbolic warping function for both transverse shear deformation and stress through the thickness coordinate. The provided two-node beam element has four degrees of freedom per node, and the discrete model maintains inter-element continuity using both C1 and C0 continuities for the kinematics variables. As a result, the isoparametric coordinate system is used to produce the elementary stiffness, geometric, and mass matrices in order to improve the current formulation. The governing equations are derived from the variational principle's weak version. In accordance with the power-law form, the material characteristics of functionally graded beams utilized change continuously over the beam thickness. The excellent performance of the developed beam element is shown by comparing recent findings to those predicted earlier by other existing theories. Furthermore, detailed numerical research is conducted to investigate the impacts of boundary conditions, power-law index, and span-to-height ratio on the free vibration and buckling responses of FG beams. Numerical findings indicate that evaluating the mechanical behavior of FG beams is difficult due to the issues mentioned earlier. [ABSTRACT FROM AUTHOR]

An investigation is performed in this paper to analyze the nonlinear thermo-electro-mechanical response of long sandwich cylindrical shells with functionally graded porous (FGP) core and thin piezoelectric actuator layers. The FGP core of the sandwich shell is assumed to be temperature- and microstructure-dependent. It is assumed that the sandwich shell is subjected to uniform lateral pressure loading in a thermo-electrical environment. The equilibrium equations of the shell with infinite length are established with the aid of the virtual displacement principle and von Kármán kinematic assumptions. The governing equations are obtained in terms of displacement components based on the first-order shear deformation model of shallow cylindrical shells and the modified couple stress theory. These nonlinear differential equations are analytically solved for a sandwich shell having both the simply-supported and clamped–clamped edge conditions by employing a two-step perturbation technique. Analytical closed-form solutions are determined as a relationship including the load parameter and the mid-span deflection. The comparison examples are made with the existing results in the literature for a simple functionally graded shell, where good agreement is obtained. It is shown that the nonlinear response of the sandwich shell is highly dependent upon the temperature variation, power law index, porosity coefficient, couple stress parameter, piezoelectric layers, and geometrical parameters of the shell. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamic behavior of micro/nanobeams made of two-dimensional functionally graded porous material (2DFGPM) under accelerated, decelerated, and uniform moving harmonic load, using surface elasticity and modified couple stress theories. The key feature of this formulation is that it deals with a higher order shear deformation beam theory. The non-classical equilibrium equations are developed using Lagrange's equation and the concept of physical neutral surface. The equations of motion are derived using the same approach, accounting for the porosity effect and the modified power-law distribution of material properties. The trigonometric Ritz method is used with sinusoidal trial functions for the displacement field, and the Newmark method is applied to obtain the dynamical response of 2DFGPM nanobeams. The results are compared with previous studies, and the impact of critical parameters such as gradation indices, volume fraction ratio, pattern of porosity, velocity, frequency, and motion type of the applied force are explored. This study highlights the importance of considering the porosity effect, as neglecting it can lead to significant errors in the predicted results. Additionally, the study found that the accelerated and decelerated motions of the applied load have a greater impact on the dynamical deflection of 2DFGPM nanobeams than the uniform motion. The findings of this study can provide guidance for the optimal design of micro/nanobeams subjected to a moving force with multifunctional properties. [ABSTRACT FROM AUTHOR]

• Homogenisation effects on the vibrations of mutlilayered microbeams with an AFG core and metal foam face layers are studied. • Differences in natural frequencies between homogenisation schemes vary with varying power gradation constant. • Higher length scale parameter leads to larger differences in natural frequencies between homogenisation schemes. • Relationship between the rotational natural frequency and the functionally graded core thickness is not linear. This study assesses the significance of homogenisation models in theoretically analysing the vibrations of three-layered microbeams with a core composed of axially functionally graded (AFG) material and with upper and lower face layers composed of metal foam material, especially when the third order shear deformation beam theory and the modified couple stress theory are used. The material of the core is assumed to vary following a power gradation profile. The range of homogenisation schemes, including the Voigt model, Reuss model, Voigt-Reuss-Hill model, Tamura model, Mori-Tanaka model, lower and upper bounds of Hashin-Shtrikman, and the local representative volume element (LRVE) model, are utilised to approximate the material properties of the AFG core. The upper and lower layers of metal foams are modelled using the closed-cell and open-cell solid porosity models. The coupled motion equations are solved for the natural frequencies of the system for the transverse, rotational and axial directions. A software-based finite element analysis (FEA) study of two simplified macrobeam systems was undertaken and the agreement between the FEA and numerical results, using the presented theoretical method, is found to be excellent. It has been confirmed that the homogenisation schemes have a notable effect on the mechanical properties of the AFG core, and hence on the coupled translational-rotational motion's natural frequencies. The largest difference in natural frequencies between different homogenisation schemes is found with a power gradation constant of approximately 0.53. A larger disparity of natural frequencies between different homogenisation methods was seen with an increase in the thickness of the AFG core and the microbeam's length-scale parameter of multilayered porous microbeam. The results of this study highlight the significance of homogenisation scheme employed when investigating the vibrations of a multilayered microbeam with an AFG core and metal foam porous face layers. [ABSTRACT FROM AUTHOR]

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