Temperature-dependent Material Properties Research Articles

Implementation of inverse method for identification of process parameters in a laser heating process

Changes in process parameters can alter the temperature data of a solid body during the laser heating process. This paper proposes an inverse method to determine the laser heating parameters, namely, sheet width, sheet thickness, laser power, and scan speed of the work specimen for the given temperature response which is assigned by the user. The method uses an analytical tool on moving heat source as a forward model capable of real-time temperature prediction of the sheet under the laser heating process. The effectiveness of the present forward model that incorporated the temperature-dependent material properties is tested by experimental findings performed on Al 6061-T6 sheets. Next, an iterative search process based on heuristic method is carried out for satisfying a prescribed temperature response by the optimization of unknown parameters. To illustrate the implementation and assess the practicality of the inverse method, two examples based on laser heating applications are used. The method proposed herein recover the unknowns for the prescribed temperature response after a few iterations, provides an efficient way to optimize the laser heating process. Additionally, the effect of measurement error on the findings of the inverse problem is addressed.

Temperature-dependent thermal buckling and free vibration behavior of smart sandwich nanoplates with auxetic core and magneto-electro-elastic face layers

AbstractThis article addresses the thermomechanical thermal buckling and free vibration response of a novel smart sandwich nanoplate based on a sinusoidal higher-order shear deformation theory (SHSDT) with a stretching effect. In the proposed sandwich nanoplate, an auxetic core layer with a negative Poisson’s ratio made of Ti-6Al-4V is sandwiched between Ti-6Al-4V rim layers and magneto-electro-elastic (MEE) face layers. The MEE face layers are homogenous volumetric mixtures of cobalt ferrite (CoFe2O4) and barium titanate (BaTiO3). The mechanical and thermal material properties of the auxetic core and MEE face layers are temperature-dependent. Using Hamilton’s principle, governing equations are constructed. To characterize the size-dependent behavior of the nanoplate, governing equations are adapted with the nonlocal strain gradient theory (NSGT). By applying the principles of Navier’s technique, closed-form solutions are obtained. Parametric simulations are carried out to examine the effects of auxetic core parameters, temperature-dependent material properties, nonlocal parameters, electric, magnetic, and thermal loads on the free vibration and thermal buckling behavior of the nanoplate. According to the simulation results, it is determined that the auxetic core parameters, temperature-dependent material properties, and nonlocal factors significantly affect the thermomechanical behavior of the nanoplate. The outcomes of this investigation are expected to contribute to the advancement of smart nano-electromechanical systems, transducers, and nanosensors characterized by lightweight, exceptional structural integrity and temperature sensitivity. Also, the auxetic core with a negative Poisson’s ratio provides a metamaterial feature, and thanks to this feature, the proposed model has the potential to be used as an invisibility technology in sonar and radar-hiding applications.

Nonlinear transient coupled thermo-electromechanical dynamic responses of the piezoelectric structure with the high-order temperature-dependent material properties

This work aims to study the nonlinear transient coupled thermo-electromechanical dynamic responses of the piezoelectric structure with the high-order temperature-dependent material properties. The multi-field coupling nonlinear model is established based on the non-Fourier thermoelasticity theories by introducing the function of high-order temperature dependency of the arbitrary material property. The virtual work principle and the nonlinear finite element approach are proposed to investigate the two-dimensional case of the orthotropic rectangular piezoelectric plate of the crystal class mm2 subjected to the zonal transient heating loads. The influences of the high-order temperature-dependent material parameters on the structural responses and wave propagations are discussed.

Hygrothermal buckling analysis of thin rectangular FGM plate with variable thickness

PurposeThis paper aims to contribute novel insights into the analysis of thin functionally graded material (FGM) plates with variable thickness, considering both temperature-dependent and independent material properties, focusing on critical linear buckling temperature rise and the effect of critical linear moisture for various moisture concentrations.Design/methodology/approachThe study derives stability and equilibrium equations for thin rectangular FGM plates under hygrothermal loading, employing classical plate theory (CPT). Buckling behavior is examined using Galerkin’s method to obtain pre-buckling force resultants.FindingsThe findings highlight significant increases in critical buckling temperature with aspect ratio, distinct temperature sensitivity between materials and increasing moisture susceptibility with larger aspect ratios. These insights inform material selection and design optimization for FGM plates under hygrothermal loading, enhancing engineering applications.Research limitations/implicationsThis research primarily focuses on hypothetical scenarios and mathematical model development and analysis.Originality/valueThis paper presents original contributions in the field by addressing the hygrothermal buckling analysis of thin FGM rectangular plates with variable thickness, utilizing CPT, thereby enriching the understanding of structural behavior in varying environmental conditions.

Recent developments in modeling and analysis of rotating functionally graded panels: A review

This article presents a comprehensive review on recent developments in the techniques for modeling and exploration of rotating functionally graded material (FGM) panels carried out between periods 2000 to 2023. Special attention is given on literature pertaining to analysis of rotating FGM panels subjected to thermo-mechanical loading. This study scrutinizes the advancements made in analysis of panels such as beam, plate, shell and blades that includes effects like porosity, thermal stress, and piezo-electric in the mathematical model. The present article also highlights the importance and ease in implementation of rule of mixture for calculation of different temperature dependent material properties used in the analysis of rotating FGM panels. An in-depth review of literature clearly indicates the importance of taking thermal effect in the estimation of elastic properties for accurate analysis of rotating FGM panels. Further, a detailed analysis of temperature profile viz., linear/non-linear, is carried out. Finally, the article concludes with the future areas that need to be explored for the analysis of rotating FGM panels.

Experimental study of in-fire and post-fire material response of high-strength aluminium alloys

This paper presents an experimental study on the residual material properties of high-strength aluminium alloys in and after fire. A testing programme was firstly conducted on grade 7075-T6 high-strength aluminium alloy, consisting of 13 in-fire and 24 post-fire coupon tests, to derive the material stress–strain responses at and after exposure to elevated temperatures ranging from 20 oC to 550 oC. The key temperature-dependent material properties including stiffness and strengths were determined from the measured stress–strain curves and normalised by their room-temperature counterparts, resulting in a series of in-fire and post-fire retention factors. These experimentally obtained retention factors were used to analyse the effects of elevated temperatures on the residual stiffness and strengths of high-strength aluminium alloys. The design in-fire retention factors, as given in the European, American and Chinese standards, and the existing predictive models in previous studies for the post-fire retention factors, were also quantitatively and qualitatively assessed based on the test data. They were found to be inapplicable due to less accuracy; especially when used for predicting the in-fire Young’s moduli, a 25% over-prediction can be yielded, leading to unsafe design. To address the shortcoming, a series of predictive models were developed to offer accurate predictions of the in-fire and post-fire residual stiffness and strengths of high-strength aluminium alloys, with the mean test-to-prediction ratios ranging from 0.995 to 1.074 for different in-fire and post-fire material properties and the design accuracy improved by at least 15% than existing design models. The Then, a two-stage Ramberg–Osgood material model that was proposed for describing the room-temperature stress–strain curves of structural aluminium alloys was considered in this study, with its applicability to high-strength aluminium alloys assessed. The considered Ramberg–Osgood model was found to well predict the in-fire and post-fire stress–strain curves of high-strength aluminium alloys. The proposed models for retention factors and stress–strain curves can be further assessed based on more test data on other new high-strength aluminium alloy grades. Future research can focus on developing new coating technologies and optimising existing treatments to improve the fire performance of high-strength aluminium alloy structures.

Effect of bi-directional material gradation on thermo-mechanical bending response of metal-ceramic FGM sandwich plates using inverse trigonometric shear deformation theory

PurposeThe purpose of this study is to investigate the bending analysis of metal (Ti-6Al-4V)-ceramic (ZrO2) functionally graded material (FGM) sandwich plate with material property gradation along length and thickness direction under thermo-mechanical loading using inverse trigonometric shear deformation theory (ITSDT). FGM sandwich plate with a ceramic core and continuous variation of material properties has been modelled using Voigt’s micro-mechanical model following the power law distribution method. The impact of bi-directional gradation of material properties over the bending response of FGM plate under thermo-mechanical loading has been investigated in this work.Design/methodology/approachIn this study, gradation of material properties for FGM plates is considered along length and thickness directions using Voigt’s micromechanical model following the power law distribution method. This type of FGM is called bi-directional FGMs (BDFGM). Mechanical and thermal properties of BDFGM sandwich plates are considered temperature-dependent in the present study. ITSDT is a non-polynomial shear deformation theory which requires a smaller number of field variables for modelling of displacement function in comparison to poly-nominal shear deformation theories which lead to a reduction in the complexity of the problem. In the present study, ITSDT has been utilized to obtain the governing equations for thermo-mechanical bending of simply supported uni-directional FGM (UDFGM) and BDFGM sandwich plates. Analytical solution for bending analysis of rectangular UDFGM and BDFGM sandwich plates has been carried out using Hamilton’s principle.FindingsThe bending response of the BDFGM sandwich plate under thermo-mechanical loading has been analysed and discussed. The present study shows that centre deflection, normal stress and shear stress are significantly influenced by temperature-dependent material properties, bi-directional gradation exponents along length and thickness directions, geometrical parameters, sandwich plate layer thickness, etc. The present investigation also reveals that bi-directional FGM sandwich plates can be designed to obtain thermo-mechanical bending response with an appropriate selection of gradation exponents along length and thickness direction. Non-dimensional centre deflection of BDFGM sandwich plates decreases with increasing gradation exponents in length and thickness directions. However, the non-dimensional centre deflection of BDFGM sandwich plates increases with increasing temperature differences.Originality/valueFor the first time, the FGM sandwich plate with the bi-directional gradation of material properties has been considered to investigate the bending response under thermo-mechanical loading. In the literature, various polynomial shear deformation theories like first-order shear deformation theory (FSDT), third-order shear deformation theory (TSDT) and higher-order shear deformation theory (HSDT) have been utilized to obtain the governing equation for bending response under thermo-mechanical loading; however, non-polynomial shear deformation theory like ITSDT has been used for the first time to obtain the governing equation to investigate the bending response of BDFGM. The impact of bi-directional gradation and temperature-dependent material properties over centre deflection, normal stress and shear stress has been analysed and discussed.

Finite element simulation and experimental investigation of in-situ laser-assisted diamond turning of monocrystalline silicon

While the effectiveness of in-situ laser-assisted diamond turning (In-LAT) for promoting the ductile machinability of monocrystalline silicon has been demonstrated, the underlying cutting mechanisms remain inadequately understood. In this study, we investigate the fundamental mechanisms involved in the In-LAT of monocrystalline silicon by finite element (FE) simulations and experiments. Specifically, a FE model of In-LAT of monocrystalline silicon is developed, which incorporates a Drucker–Prager constitutive model to address the brittle fracture of the material, as well as temperature-dependent materials properties to address the thermal softening effect. Furthermore, experiments of In-LAT of monocrystalline silicon are conducted with the self-developed In-LAT device, including tapering cutting and end face cutting. Simulation results demonstrate that In-LAT significantly increases the critical depth of cut for the brittle-to-ductile transition of monocrystalline silicon in tapering cutting mode by 72.2% compared to conventional cutting, accompanied with significantly reduced cutting forces, continuous chip profile and reduced surface brittle damage. The promotion of ductile machinability of monocrystalline silicon under In-LAT is attributed to the reduction and dispersion of stress in the cutting zone, which is in contrast to the significant stress concentration at the rake face and cutting edge in conventional cutting. And simulation results also provide an optimal temperature field of 900 K for the In-LAT of monocrystalline silicon, above which the excessive plastic flow accompanied by thermal accumulation results into deteriorated surface roughness. These findings provide valuable insights for understanding the cutting mechanisms of In-LAT and the parameter optimization for In-LAT application.

Nonlinear thermoelastic wave propagation in general FGM sandwich rectangular plates

The present work is dedicated to investigating the thermoelastic wave propagation behavior of sandwich rectangular plates (SRP) made of functionally graded material (FGM). The main contribution lies in the partial modification of basic theoretical expressions and solution methods to improve the accuracy of practical system models. An analytical model with three types of general configurations is established. The porosity distribution in FGM layers depends on the degree of mixture of the constituent materials, with the FGM layers without porosity taken as a reference model. The effect of porosity within FGMs is addressed through a refined analytical formulation of material properties, and the temperature-dependent material properties of FGM sandwich structures (FGMSS) maintain continuity through the thickness. This improved framework introduces a porosity function encompassing three distinct structural and geometrical functions: the core-to-thickness ratio (CTR), porosity volume fraction (PVF), and porosity distribution function (PDF). It is worth mentioning that the theoretical expressions maintain good continuity and reliability under the influence of thermal conditions and system parameters of the proposed structures. Furthermore, considering the generation of thermal strain energy (TSE) caused by thermal expansion of the structure in the normal direction, an improved analytical approach for determining TSE in rectangular plate structures is then investigated by introducing the Green's nonlinear strain (GNS). Hamilton's principle is applied to derive the wave motion equations and analytical solutions for the wave dispersion relations are derived. Furthermore, accurate numerical simulation is performed and the solution is verified with data available in published resources. In addition, we present a systematic parametric analysis to examine the effects of porosity, configuration, power-law exponent (PLE), PVF, CTR, temperature, and wave number on the thermoelastic wave propagation behavior of FGMSRP.

Generalized thermoelastic wave response in a hollow cylinder with temperature-dependent properties based on the memory-dependent derivative of the heat conduction model

High-temperature pipelines are susceptible to defects due to the long-term service in high-temperature environments. The guided wave technology is promising for online non-destructive testing. Before implementing it in engineering, it is essential to better understand guided wave characteristics, especially attenuation, which significantly decreases the test distance and the resolution. However, describing the large attenuation is challenging due to the strong thermoelastic coupling, resulting in limitations of available models. To address these limitations, this paper aims to introduce a memory-dependent generalized thermoelastic model for investigating guided waves propagating in a hollow cylinder with temperature-dependent material properties. The analytical solutions are obtained using the Legendre polynomial method. The influence of the memory-dependent effect, temperature variation, and boundary conditions are studied. Some interesting findings are revealed: (1) The time delay factor is more dominant when adjusting κ and n to accurately describe guided wave propagation at high temperatures. (2): The mode conversion is accompanied by the attenuation and group velocity jump when the adjacent flexural torsional and longitudinal modes intersect, which is advisable to avoid when choosing the excitation frequency. (3) The relationship between phase velocity and attenuation versus temperature for quasi-elastic modes is nonlinear, while that for thermal modes is approximately linear.

Extended constant life diagrams for low cycle fatigue and creep-fatigue assessments of high-temperature structures

Over the decades, the constant life diagram has become an important tool for engineering design and assessment. For specific materials, the effect of mean stress and stress amplitude on the fatigue life is considered in traditional constant life diagrams. In this study, the concept of the structural constant creep-fatigue life diagram is proposed for engineering structures subjected to cyclic loads in high-temperature environments. By integrating constant fatigue and creep-fatigue life curves into the traditional Bree diagram, we offer an efficient and reliable approach that enables quick determination of structural life and corresponding failure mechanisms. To provide a one-stop solution for the evaluation of constant fatigue/creep-fatigue life curves, an extended Unified Procedure for Fatigue and Ratchet Analysis (eUPFRA) has been proposed based on the Linear Matching Method (LMM) framework. Case studies on engineering components have also been performed with consideration of the cyclic hardening effect, temperature-dependent material properties and various damage models. The impact of the target life and creep dwell time is further investigated, as well as the creep-fatigue interaction mechanism. Verification against ABAQUS step-by-step inelastic analysis has finally been conducted, confirming the precision and efficiency of the eUPFRA.

Coupled thermal-mechanical analysis of power electronic modules with finite element method and parametric model order reduction

This work presents a new approach for performing a parametric study and examining nonlinear material behaviours of a coupled thermal-mechanical model of a Power Electronics Module (PEM) by integrating the Finite Element Method (ANSYS-FEM) with Parametric Model Order Reduction (pMOR). The considered coupling method solves the thermal and structural models concurrently compared to the widely practised sequential coupling method. Instead of constant parameter values, which are generally regarded for pMOR studies, the temperature-dependent material properties of the wire material have been parametrised in the work using the pMOR method. A generalised 2D model has been regarded here for thermal-mechanical analysis with the pMOR approach, parametrising temperature-dependent coefficient of thermal expansion (CTE) and Young’s modulus (E) of the wire material to explore their impact on wire bonds. The matrix interpolation method has been applied here for the pMOR study, and PRIMA, a Krylov subspace-based model order reduction (MOR) technique, has been exercised for local model order reductions. A new efficient process of matrix interpolation, based on the Lagrange interpolation technique, has been developed to implement matrix interpolation in the parametric reduced order model (pROM). The local reduced order models (ROMs) have a degree of freedom (DOF) of just 8, compared to the full-order models’ (FOMs) of 50,602. The pROM provides an excellent solution and reduces computational time by 84% for the presented case.

Thermo-mechanical finite element analysis of the solid-state metal deposition via lateral friction surfacing

Lateral friction surfacing (LFS) is a novel variation of the friction surfacing (FS) process for solid-state fabrication of ultra-thin and smooth metal coatings. In the LFS technique, pressing the lateral side of a rotating rod against the substrate's surface generates frictional heat and plastic deformation, leading to the deposition of consumable material from the lateral surface of the rod onto the substrate. This study presents numerical analysis for such a complex coupled thermo-mechanical process to investigate the distribution of various variables such as temperatures, local pressure, stress, and strain throughout the consumable rod and substrate. A finite element model of the process was developed through ABAQUS/Explicit method to investigate the thermo-mechanical response of rod and substrate materials by incorporating various features such as process parameters, mechanical behaviors of materials, temperature-dependent material properties, and failure criteria. The finite element model was validated by conducting experimental analysis using the same materials and values of process parameters. The finite element simulation results were consistent with previous experiments and affirmed that process temperature is lower than in conventional FS and localized in a small area, which can reduce thermal impacts on the consumable rod and substrate materials. Although the majority of the frictional heat was transferred to the Al6061-T6 rod due to its higher thermal conductivity, it was revealed that the maximum process temperature occurred on the mild steel substrate. The results of the study demonstrate that selecting an appropriate dwell-phase duration not only enhances the material's temperature to facilitate improved deposition but also ensures more consistent contact across all points along the rod's side, resulting in a uniform deposition.

Incorporating non-linear effects in fast semi-analytical thermal modelling of powder bed fusion

The usefulness of semi-analytical thermal models for predicting the connection between process, microstructure and properties in powder bed fusion has been well illustrated in recent years. Such an approach provides predictions that are orders of magnitude more computationally efficient than numerical approaches. However, the opportunity to make predictions that span several orders of magnitude in space and time comes at the cost of significant simplifications, limiting fully quantitative predictions without empirical calibration. This approach relies on the solution to a linear problem meaning that first order non-linear effects induced by e.g. the temperature dependence of material properties and surface boundary conditions, are not incorporated. Here, we revisit these limitations and highlight ways that temperature-varying material properties and radiative heat loss from the melt pool can be systematically accounted for without prior calibration. These corrections, made with an eye to minimizing additional computational overhead, bring the technique’s predictive capability much closer to that of higher fidelity thermal simulations without a significant computational cost. Quantitative comparisons to experiments are used to illustrate the important impact of including such corrections.

Combined effect of temperature dependent material properties and boundary conditions on non-linear thermal stability of porous FG beams

Combined effect of temperature dependent material properties and boundary conditions on non-linear thermal stability of porous FG beams

Transient thermal stress analysis of a thin rotating FGM blade based on the exact shear correction factor: a comparison of ROM and LRVE homogenization models

This work is an attempt to develop a simple and accurate finite element formulation based on first-order shear deformation theory (FSDT) for the transient thermal stress analysis of a pre-twisted and tapered thin rotating functionally graded material (FGM) blade, induced due to the thermal shock. The neutral surface of the FGM blade is taken as the reference plane and the exact shear correction factor is obtained from the equivalent energy principle. The temperature-dependent material property at a point in the thickness direction is estimated according to the rule of mixture (ROM) and the Local representative volume elements (LRVE) homogenization model. A finite element formulation using FSDT in conjunction with the eight-noded isoparametric element, taking five degrees of freedom is developed. The top layer of the thin FGM blade is subjected to a thermal shock and the bottom layer is kept at the ambient temperature. The governing equation for the present formulation is obtained using Hamilton’s principle. The accuracy of the present finite element formulation is established by comparing the results with the benchmark results. The parametric studies are conducted to investigate the effect of the angle of twist, variable chord and span, rotational speed, and accurate shear correction factor on the transient thermal stresses due to the thermal shock. Notably, there can be significant differences in the transient thermal stresses calculated by the two homogenization models viz., ROM and LRVE. Also, it is important to consider the exact shear correction factor in the formulation.

A slice model for thermoelastic analysis of porous functionally graded material sandwich beams with temperature-dependent material properties

Porosity usually occurs in functionally graded materials (FGMs) during the fabrication process. Its effects on the thermomechanical behaviors of FGM structures are worth studying. In this work, heat transfer and thermoelastic behaviors of porous FGM sandwich beams with temperature-dependent material properties are examined. The effective material properties are approximately estimated by the modified Voigt mixture rule. Because of the continuously varied material properties across the thickness direction, it is impractical to seek exact solutions for the beam. By proposing a slice model in which the face and core layers are divided into numerous thin slices, the material properties of each slice can be treated as uniform. Based on the model, the through-thickness temperature distribution is first obtained by using an iteration algorithm. Then the two-dimensional (2-D) thermoelasticity equations are analytically solved by using the state space method and Fourier series expansion method. The correctness of the proposed model is checked through comparison with results reported in previous works. The effects of some key factors such as the temperature dependence of material properties, volume fraction, and porosity on the thermomechanical behaviors of the beam are comprehensively studied. It is shown that with the increase of porosity, the thermal resistance capacity of the beam is enhanced yet the bending stiffness is weakened.

Fire Behavior of Concrete-Filled Hollow Section Columns with High Strength Bar-Bundle as Core

AbstractConcrete-filled hollow section (CFHS) columns with a solid steel core have gained popularity in the construction of tall buildings due to their robust load-bearing capacity, slender design, ease of prefabrication, and exceptional structural fire resistance. In this research paper, we introduce an innovative approach aimed at enhancing the structural performance of these columns. Our method involves replacing the solid steel core with high-strength bar bundles and substituting concrete with grout to achieve superior fire resistance. These modified columns are referred to as “bar-bundle columns.” The paper presents the results of extensive fire tests conducted on three bar-bundle columns, each with different bar-bundle sizes, quantities, and configurations. Additionally, we determine the temperature-dependent material properties of the high-strength steel used for reinforcing bars and the thermal properties of the grout used as a filler through standard experimental tests, which are crucial for numerical simulations. An advanced nonlinear finite element model is describe which is capable of predicting the fire behavior of bar-bundle columns. Finally, this numerical model is employed to conduct parametric analyses and propose a simplified design model for bar-bundle columns under fire conditions.Our findings indicate that the bar-bundle configuration and using grout as a filler significantly delays the heating of the steel core, resulting in enhanced fire resistance when compared to CFHS columns with a solid steel core. The simplified method proposed in this study can be used to estimate the fire resistance of slender bar bundles, but further experimental testing could further refine and improve its accuracy.

Temperature Monitoring of Through-Thickness Temperature Gradients in Thermal Barrier Coatings Using Ultrasonic Guided Waves

Ultrasonic guided waves offer a promising method of monitoring the online temperature of plate-like structures in extreme environments, such as aero-engine nozzle guide vanes (NGVs), and can provide the resolution, response rate, and robust operation that is required in aerospace. Previous investigations have shown the potential of such a system but the effect of the complex physical environment on wave propagation is yet to be considered. This article uses a numerical approach to investigate how thermal barrier coatings (TBCs) applied to the surface of many components designed for extreme thermal conditions will affect ultrasonic guided wave propagation, and how a system can be employed to monitor through-thickness temperature changes. The top coat/bond coat boundary in NGVs has been shown to be a temperature critical point that is difficult to monitor with traditional temperature sensors, which highlights the potential of ultrasonic guided waves. Differences in application method and layer thickness are considered, and analysis of through-thickness displacement profiles and dispersion curves are used to predict signal response and determine the most suitable mode of operation. Heat transfer simulations (COMSOL) have been used to predict temperature gradients within a TBC, and dispersion curves have been produced from the temperature dependant material properties. Time dependant simulations of wave propagation are in good agreement with dispersion curve predictions of wave velocity for the two lowest order modes in three thicknesses of TBC top coat (100, 250, and 500 μm\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\upmu \\hbox {m}$$\\end{document}). When wave velocity measurements from the simulations are compared to dispersion curves generated at isotropic temperatures, the corresponding temperature represents the average temperature of a gradient system well. Such a measurement system could, in principle, be used in conjunction with surface temperature measurement systems to monitor through-thickness temperature changes.

Tension buckling and postbuckling of nanocomposite laminated plates with in-plane negative Poisson’s ratio

Abstract Mechanical metamaterials with negative Poisson’s ratio (NPR) have emerged as a novel class of engineering material, and have attracted increasing attention in various engineering sectors. Most studies available on the buckling problem of laminated plates with positive or NPR are those under uniaxial compression. Here, we report that the buckling phenomenon may occur for auxetic nanocomposite laminated plates under uniaxial tension when the unloaded edges of the plates are immovable. Two types of nanocomposites are considered, including graphene/Cu and carbon nanotube/Cu composites. Governing equations of the auxetic nanocomposite laminated plates are formulated based on the framework of Reddy’s higher-order shear deformation theory. In modeling, the von Kármán nonlinear strain–displacement relationship, temperature-dependent material properties, thermal effects, and the plate–substrate interaction are considered. The explicit analytical solutions for postbuckling of auxetic nanocomposite laminated plates subjected to uniaxial tension are obtained for the first time by employing a two-step perturbation approach. Numerical investigations are performed for tension buckling and postbuckling behaviors of auxetic nanocomposite laminated rectangular plates with in-plane NPR rested on an elastic substrate under temperature environments.