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The dynamic response of a two-dimensional generalized thermoelastic diffusion problem for a half-space is investigated in the context of the generalized thermoelastic diffusion theory. The half-space is subjected to a thermal shock and a chemical potential shock on its bounding surface. The governing equations of this problem are formulated, and due to the complexity of the equations, a numerical method, i.e., hybrid Laplace transform-finite element method, is used to solve them. The non-dimensional temperature, displacement and chemical potential are obtained and illustrated graphically. The results show that the non-zero values of all the considered variables are only in a bounded region and vanish identically beyond this region, and the propagating speed of diffusive wave is larger than that of thermoelastic wave. [ABSTRACT FROM AUTHOR]

Abstract: The generalized thermoelastic theory with thermal relaxation, in the context of Lord and Shulman theory, is used to investigate the magneto-thermoelastic problem of a thin slim strip placed in a magnetic field and subjected to a moving plane of heat source. The generalized magneto-thermoelastic coupled governing equations are formulated. By means of the Laplace transform and numerical Laplace inversion, the governing equations are solved. Numerical calculations for the considered variables are performed and the obtained results are presented graphically. The effects of moving heat source speed and applied magnetic field on temperature, stress and displacement are studied. It is found from the graphs that the temperature, thermally induced displacement and stress in the strip are found to decrease at large heat source speed, and the magnetic field significantly influences the variations of non-dimensional displacement and stress. However, it has no effect on the non-dimensional temperature. [Copyright &y& Elsevier]

• TED is first established in nonlocal strain gradient theory with dual-phase-lag model. • The equations with scale effects on TED are solved by complex frequency method. • The effects of scale parameters and material properties on TED are examined. • Both stiffness hardening and softening effects are captured. • The present method is useful to evaluate TED in nanomechanical resonators. Thermoelastic damping (TED), as a main source of intrinsic energy dissipation, is crucial to the design of the micro/nano-devices and -systems with higher quality factor (Q -factor). However, the classical analysis model of TED fails in micro/nano-scale due to the influence of small-scale effect. The present article focuses on investigating the influence of scale effect on the TED of micro-beam resonators by considering stress nonlocal and higher-order strain gradient effects. Firstly, the governing differential equations are formulated by employing the nonlocal strain gradient theory (NSG) in conjunction with the dual-phase-lag (DPL) heat conduction model. According to the assumption of vibration mode and the boundary conditions, the size-dependent Q -factor expression of TED is derived by the complex frequency method. Finally, the influences of various parameters on the TED of micro-beam resonators, such as nonlocal parameter, length scale coefficient, slenderness ratio and material type, are discussed in detail. And then, the analysis results are compared with the TED of classical thermal-mechanical model. This article provides a novel theoretical analysis model of the TED in micro/nano-meter scale field, which has practical significance in the design of high-efficiency devices and systems. [ABSTRACT FROM AUTHOR]

Abstract: The theory of generalized thermoelasticity, based on the theory of Lord and Shulman with one relaxation time, is used to study the electromagneto-thermoelastic interactions in an infinitely long perfectly conducting solid cylinder subjected to a thermal shock on its surface when the cylinder and its adjoining vacuum is subjected to a uniform axial magnetic field. The cylinder deforms because of thermal shock, and due to the application of the magnetic field, there result an induced magnetic and an induced electric field in the cylinder. The Maxwell''s equations are formulated and the generalized electromagneto-thermoelastic coupled governing equations are established. By means of the Laplace transform and numerical Laplace inversion the problem is solved. The distributions of the considered temperature, stress, displacement, induced magnetic and electric field are represented graphically. From the distributions, it can be found the electromagnetic-thermoelastic coupled effects and the wave type heat propagation in the medium. This indicates that the generalized heat conduction mechanism is completely different from the classic Fourier''s in essence. In generalized thermoelasticity theory heat propagates as a wave with finite velocity instead of infinite velocity in medium. [Copyright &y& Elsevier]

• A new rate-dependent constitutive model of thermo-electromechanical coupling is developed within extended thermodynamics. • Structural responses to multilayered laminated piezoelectric composites with imperfect interfacial conditions are investigated. • Strain and electric rates efficiently eliminate abrupt jumps of structural responses at elastic and thermal wave fronts. • Rationally adopting parameters ratios remarkably lift stress isolation and electric energy harvesting. Thermo-electromechanical coupling analysis at micro/nano-seconds appears to be particularly important, where strain and electric relaxation effects will increase significantly in such case. So far, although temperature-rate-dependent theory of piezoelectric thermoelasticity has been historically proposed, it may be no longer hold anymore as relaxation effects both in electrical and strain fields have not been fully considered yet. This work mainly contributes to constitutive modeling of a novel rate-dependent piezoelectric thermoelasticity by considering time-derivatives terms of the elastic strain, relative temperature, and electric intensity associated with related relaxation time parameters. Constitutive and field equations are strictly derived via extended thermodynamics. Newly developed theoretical model is applied to analyze structural thermo-electromechanical responses of multilayered laminated piezoelectric smart composites accounting for contact imperfection and material parameters via a semi-analytical integrated transformation technique. Dimensionless results reveal that the properly selecting thermal/stain/electric relaxation time parameter or considering non-idealized boundary conditions at interface of multilayered laminated piezoelectric smart composites will maximally enhance the electric energy harvesting, realize the displacement control, and improve the harmful stress isolation. [ABSTRACT FROM AUTHOR]

• A novel TED model is established. • Analytical expression of the TED model is obtained. • The TED model can reduce to the classical TED model. • A critical thickness is proposed. • Small scale significantly improves TED within the critical thickness. Thermoelastic damping (TED) is one of the main energy dissipation sources of high performance resonators at room temperature, however, the classical TED model fails at the nano-scale due to the influence of small scale effect. In this paper, a novel TED model is proposed to estimate the impact of both mechanical and thermal small scale effects on TED of nano-resonators. The surface elastic theory and the dual-phase-lag heat conduction model (DPL model) are first combined to establish the TED model. Analytical expression of the TED model is derived, which can reduce to the classical TED model. In numerical simulations, a critical thickness is proposed to identify the influence of small scale effect on TED. Small scale effect significantly improves TED of resonators within the critical thickness, which however can be neglected as the resonator thickness is greater than the critical thickness. Moreover, surface effect has stronger effect than non-Fourier heat conduction on improving TED of nano-resonators. Additionally, influences of the other key factors on TED are examined in detail. This paper provides a more reasonable theoretical approach to estimate TED in the design of high performance nano-resonators. [ABSTRACT FROM AUTHOR]

The Stefan conditions are suitable for describing the solid-liquid phase change processes with moving interface. However, the existing literature only focuses on the Stefan problem of heat conduction and does not involve the thermo-mechanical coupling effects. In this work, the generalized thermoelastic Stefan problem with spatio-temporal nonlocal effect is investigated. The solid-liquid phase change of silicon with picosecond pulse laser machining is depicted by the Stefan interface conditions. We find the solutions making use of Laplace transformation and Laplace numerical inverse transformation. The temperature distribution at the moment of surface melting is seen as the initial state of the second phase. The distributions of transient thermoelastic responses under different laser intensities, pulse widths, fractional order parameters, spatial nonlocal parameters and time are obtained and expressed graphically. • The introduction of Stefan conditions into the nonlocal generalized thermoelasticity. • The solid-liquid interfaces moving with time due to laser processing are considered. • The temperature at the surface melting moment is taken as the initial condition. • The heat taken away by vaporization is considered in the boundary condition. • With laser intensity increasing/duration decreasing, the transient responses increase. [ABSTRACT FROM AUTHOR]

We study the extensional vibration of composite multiferroic piezoelectric semiconductor (PS) nanoharvester driven via a time-harmonic magnetic field. A theoretical analysis about working performances of device is performed based on zero-order plate equations with surface and nonlocal effects, consisting of a nonlinear magneto-mechanical coupling constitutive model for giant magnetostrictive material Terfenol-D and a linear phenomenological theory of PS material ZnO. Numerical results indicate that the basic bahaviors (including resonant frequency, bandwidth characteristic, magneto-electric (ME) coupling effect, output power and energy conversion efficiency) of the nanoharvester, can be dramatically improved through circuit types, semiconduction, external magnetic field, pre-stress and surface effect. This work is essential and crucial for understanding the size-dependent and nonlinear mechanical behaviors of multiferroic PS nanodevices under the extremely complex magnetic field and pre-stress field environments. • A nonlinear analytical model for extensional vibration of broadband ME nanoharvester with semiconduction is established. • Dynamic manipulation for transport behaviors of carriers based on ME coupling effect is theoretically demonstrated. • A larger initial carrier density will lead to a lower output power density and resonant frequency due to stronger screening. • This work provides us some opportunities to artificially control bandwidth characteristic and output power of nanoharvester. • Size-dependent effect and corresponding critical thickness caused by surface effect are all revealed for nanoharvester. [ABSTRACT FROM AUTHOR]

Thermoelastic damping (TED) is one of the key factors for lowering the quality factor (Q-factor) of micro/nano-resonators. However, due to a complex small-scale effect and governing equations of non-homogeneous isotropic materials, the existing TED models usually focus on homogeneous isotropic micro/nano-resonators. In this paper, a closed-form TED model is derived to estimate the influence of the small-scale effect on TED of transversely isotropic micro/nano-resonators. The surface effect and the dual-phase-lag model are included to distinguish the influence of mechanical and thermal small-scale effects on TED, respectively. The obtained TED model is theoretically verified. The results indicate that TED values are underestimated if the classical TED model is employed. Moreover, a critical thickness can be determined by the frequency shift curve is proposed. The small-scale effect results in higher TED values within the critical thickness. However, since the small-scale effect has a weak influence on TED, it can be neglected when the resonator thickness is higher than the critical thickness. Additionally, the surface effect plays a dominant role in improving the TED of nano-resonators. In this paper, a more reasonable theoretical approach for estimating TED in transversely isotropic micro/nano-resonators is provided. [ABSTRACT FROM AUTHOR]

The ultrashort pulse laser is widely used in micro scale non-contact machining of nonmetallic materials because of its high energy density, short pulse duration and small heat affected zone. Ablation is the main material removal mechanism in ultrashort pulse laser processing. This motivates us to establish the f ractional d ual- p hase- l ag (FDPL) generalized thermoelastic ablation model and investigate the transient responses of silicon ablated by the picosecond pulse laser. The temperature-dependent material properties, surface recession velocity and plasma shielding effect on the subsequent laser beam have been paid more attention. In calculation, the temperature distributions at the surface melting moment and plasma formation moment are taken as the initial conditions of the next Phases. The coupled governing equations containing fractional order parameter, lag times as well as spatial nonlocal parameter are formulated and solved by Laplace transform together with its numerical inversion. The temperature, displacement and stress with different laser intensity, pulse duration, fractional order parameter, lag time ratio as well as times are obtained and illustrated graphically. The accurate thermoelastic coupling description of silicon processed by the ultrashort pulse laser is obtained, which provides a reliable theoretical guide for high-quality laser processing of nonmetallic materials. [ABSTRACT FROM AUTHOR]

In recent years there have been many papers that considered the pyroelectric effect in the investigations of thermo-mechanical coupling of piezoelectric ceramics serving in non-uniform thermal environment, particularly with extensive applications of ultrafast heating technologies (e.g., laser burst, laser ablation, etc.) in micro-machining of piezoelectric structures (e.g., piezoelectric sensor/actuator/generator/energy harvester, etc.). However, in such conditions, the existing piezoelectric thermoelasticity theories will not be applicable due to the lack of consideration of the memory-dependence feature in the constitutive relations and heat transport equation. To further refine the piezoelectric thermoelasticity models, present study develops a new theoretical model of generalized piezoelectric thermoelasticity which fully account for fractional order strain and heat conduction. By establishing constitutive equations within the extended thermodynamic framework, the governing equations are derived. In the aspect of application, the transient thermo-electromechanical responses of multi-layered piezoelectric laminated composite structure with non-idealized interfacial conditions is investigated. The effects of material constants ratio and fractional order parameters of each layer on structural responses are evaluated and summarized to offer some new insights and guidelines on the strength design, thermal protection, and vibration control of multi-layered piezoelectric laminated composite structure under ultrafast heating condition. • New theoretical model of piezoelectric thermoelastic coupling is developed. • An analytical model of multi-layered piezoelectric laminated structure is chosen. • Non-idealized interfacial conditions are considered. • Transient thermo-electromechanical responses are investigated. • Material constants ratio and strain relaxation show great effects on responses. [ABSTRACT FROM AUTHOR]

• Generalized diffusion-elasticity problems with concentration-dependent elastic modulus and diffusivity are studied. • Time-domain finite element method is applied to deal with the problem. • The principle of virtual work is performed to formulate the nonlinear finite element governing equations. • Nonlinear transient diffusion-elastic responses are investigated. • Concentration-dependent elastic modulus and diffusivity affect the nonlinear responses greatly. The investigations of mechanical-diffusion coupling are of great importance for the micro-electromechanical devices under non-uniform concentration environment, especially with the development of energy storage technology for a rapid charging system. In recent years there have been many experimental and theoretical studies show that the elastic constants and the diffusivity depend on the concentration of diffusing substances. In view of this, present work aims to study generalized diffusion-elasticity problems considering the concentration-dependent elastic constants and the diffusivity by time-domain finite element method. By using principle of virtual work, the obtained nonlinear finite element equations are solved directly in time domain to minimize precision losses in the application of integrated transformation method, and then the nonlinear solutions can be obtained. As numerical examples, the developed method is used to investigate the transient response of a thick circular plate subjected to the shock loading of the concentration. The results demonstrate that the developed method can faithfully predict the deformation of structure and most importantly the diffusive wave feature in both one-/two-dimensional solids whilst it is commonly difficult to model, especially for two-dimensional case, by using transform method. Parametric studies are performed to evaluate and discuss the effects of concentration-dependent elastic constants and diffusivity on the structural dynamic responses. [ABSTRACT FROM AUTHOR]

The absorption mechanisms of plasma plume (such as inverse bremsstrahlung, photo-ionization and Mie absorption) to ultrashort pulse laser have significantly influence on efficiency and quality of laser machining. This motivates us to establish the spatial nonlocal generalized thermoelastic model with plasma absorption mechanisms. Based on the new model, the porous sandwich composite material with perfectly bonded interface is researched. The two outer layers are made of copper and two boundaries are heated by the picosecond pulse laser. The middle layer's material properties are proportionate to those of the outer layers. By using the Laplace transformation and inverse Laplace transform, the governing equations that incorporate spatial nonlocal parameter, strain and thermal relaxation factors are solved. The transient responses, such as temperature, volume fraction field, etc., with different laser parameters, material characteristic parameter and absorption mechanisms of plasma plume are obtained and illustrated graphically. [ABSTRACT FROM AUTHOR]

In this paper, from the view of active manipulation of electronic devices, to better reveal an external stimulus field-dependent mechanical tuning methodology and mechanism on the resonance characteristic and working performance, a comprehensive analytical model and theoretical solution of flexoelectric energy nanoharvester, driven via a time-harmonic magnetic field and thermal field, have been developed and established, in which, the coupled extensional and flexural vibration, flexoelectricity and surface effect as well as nonlinear magnetic-mechanical-thermo-electric coupling characteristic, are all included. After effective material constants of giant magnetostrictive material are exactly obtained, some key performance indexes (including strain gradient, output current, magneto-electric (ME) coupling coefficient, output power density, resonant frequency) of the harvesters are systematically investigated and discussed, which not only can be controled actively and tuned intelligently under applied external magnetic fields, pre-stresses and thermal fields stimuli, but also can also be dramatically enhanced and improved effectively through both flexoelectricity and surface effect. The theoretical model and solution obtained in this study are more general, which are suitable for the macroscopic and microscopic, linear and nonlinear mechanical analysises. Meanwhile, this work also provides a theoretical basis for more extensive investigations related to widely-used high frequency vibrations with shear deformation in device applications. [ABSTRACT FROM AUTHOR]

Abstract: By using the principle of virtual work, the finite element equations corresponding to the generalized thermoelasticity with two relaxation times (i.e., the G–L theory) are derived. In order to improve the accuracy of integral transform method, especially in two/three-dimension, the equations are solved directly in time-domain. As numerical examples, the developed method is used to investigate the generalized thermoelastic behavior of a slim strip and a semi-infinite plate subject to thermal shock loading. The results demonstrate that the developed method can faithfully predict the deformation of the structure and most importantly the delicate second sound effect of heat conduction in both one and two-dimensional solids whilst it is usually difficult to model, especially in two-dimensional, by using the transform method. This method can also be used to study generalized piezothermoelastic and magnetothermoelastic problems. [Copyright &y& Elsevier]

In present paper, a linear thermoelastic theory for porous materials is established by extending the existing theory, in which the strain relaxation and the thermal relaxation are included. Based on the thermodynamic laws, the constitutive relations are derived, and then the corresponding constitutive equations are obtained by specifying the generalized free energy. Further, by combining the existing theory, the non-Fourier's heat conduction law and the obtained constitutive equations, the linear thermoelastic theory for porous materials is formulated. To apply the established theory, the transient response of a half-space with voids is considered. The half-space with voids is subjected to a thermal shock and a mechanical shock simultaneously on its bounding surface. The problem is solved by means of Laplace transform and its numerical inversion. The distributions of the non-dimensional temperature, displacement, stress as well as the volume fraction field are obtained and illustrated graphically. In calculation, the effects of the thermal relaxation factor, the strain relaxation factor and the magnitude of the mechanical shock on the considered variables are examined and discussed in detail. • A new linear thermoelastic theory for porous materials is established by extending the existing theory. • The main novelty of this new theory lies in that both the strain relaxation and the thermal relaxation are included. • This new theory is formulated by means of thermodynamic laws and work-energy relation. • The application of this new theory to the thermoelastic dynamic response of a half-space with voids is presented. [ABSTRACT FROM AUTHOR]

• Ultrashort laser has obvious impacts on the heat conduction and structural response. • Comparison of results between the fractional order and memory dependent derivative. • The obtained curves agree well with the previous theoretical deduction. • The bigger contact thermal resistance leads to the larger mutation at the interface. • Kernel function and material characteristic have marked impacts on the variables. Ultrashort laser technology has been widely used in micro-machining due to its high power, precision of operation, low cost, high control and extremely short duration. This motivates us to investigate the transient response of a bi-layered structure subjected to a non-Gaussian laser beam on its bounding surface in the context of the time-fractional derivative based on generalized thermoelastic theories. Comparison studies between the fractional order and the memory-dependent derivative models are performed and the thermal contact resistance at the interface is also considered. The coupled governing equations involving with thermal relaxation time, fractional order parameter, time delay and kernel function, which can be chosen freely according to specific problems, are solved by using Laplace transform technique together with its numerical inversion. During the analysis, the first layer is selected as the copper material and the material characteristic parameters of the second layer such as the thermal conductivity, mass density and specific heat capacity are given by ratios to those of the first layer. The influences of the material characteristic parameters on the heat conduction and the structural responses are emphatically discussed, and the non-dimensional temperature, displacement as well as stress at different values of fractional order parameter, time delay factor, kernel function and thermal contact resistance are obtained and illustrated graphically. Finally, based on the obtained results, the bi-layered structure heated by a non-Gaussian laser beam may be reasonably designed in engineering. [ABSTRACT FROM AUTHOR]

The studies of the coupling of thermodiffusion and mechanical deformation in solids have aroused great interests with miniaturization of the micro/nano-electromechanical devices and wide application of ultrafast heating technologies. In such situation, it is commonly accompanied with high heat/diffusion flux and thermal/diffusion induced stress accordingly. So far, although there have been many developments and extensions of research and theorizing within the generalized thermoelastic diffusion problems, these theoretical formulations are only applicable when the strain rate is assumed to be relatively small, but this is questionable under ultrafast heating condition. The present work aims to investigate generalized thermoelastic diffusion problems with fractional order strain within the extended thermodynamic framework. For numerical evaluation, the analytical model of a sandwich structure with ideal interfacial conditions is investigated whilst its bounding surfaces are subjected to symmetrical transient heat and chemical potential shock loads. From numerical results, the effects of the fractional order parameters and material characteristic parameters of each layer on structural transient thermo-elasto-diffusive responses are also analyzed and discussed, which is expected to provide a comprehensive understanding on thermoelastic diffusive coupling and optimal design of sandwich structures under extreme fast heating condition. • Generalized thermoelastic diffusion theory with fractional strain is developed. • Transient thermoelastic diffusion responses of sandwich structure are studied. • Fractional order strain can characterize the strain relaxation feature. • Fractional order parameters have great effects on structural responses. [ABSTRACT FROM AUTHOR]

Multi-layered piezoelectric nanostructures stand as one the most promising candidates for smart nanodevices and nanocomposites which are widely used as sensors and actuators in nano-electromechanical systems due to their excellent performances in fabrication, design and energy conversion (i.e. electrical and mechanical energy). The inherent nano-sized piezoelectricity properties (e.g. enhanced piezoelectric effect and novel electrical/chemical/physical properties) enable them to be regarded as the next-generation piezoelectric materials. Present study aims to investigate the size-dependent thermo-electromechanical responses of multi-layered piezoelectric nanoplates under heating loads. In the context of nonlocal piezoelectric thermoelastic theory, a composite laminated piezoelectric plate is chosen as the analytical model whilst the coupled governing equations for each layer with size-dependent characteristic lengths of thermal, electric and elastic fields as well as non-idealized interfacial conditions are obtained, and then solved by using Laplace transformation techniques. The transient solutions obtained are applied to bi-layered piezoelectric nanoplates and the effects of size-dependent characteristic lengths and material constants ratio on structural responses are evaluated and discussed to provide a comprehensive understanding and design insights of piezoelectric nanocomposites. [ABSTRACT FROM AUTHOR]