Thermoelastic Behavior Research Articles

Investigation on the thermoelastic response of a nanobeam in modified couple stress theory considering size-dependent and memory-dependent effects

For nano/micro-scale structures, the classical continuum mechanics can’t properly depict the size-dependent effect arising in them anymore. In addition, Fourier’s law is limited in describing the heat transfer process in nano/microstructures due to its nature of predicting infinite heat speed. To amend such defects, the non-classical continuum mechanics based on the nonlocal elasticity theory and the modified couple stress theory incorporating the non-Fourier heat transfer model with memory-dependent effect is formulated to characterize the thermoelastic behaviors in micro/nano-scale system in the present work. Then, the model is used to study the dynamic response of an Euler-Bernoulli nanobeam subjected to a ramp-type heating. The corresponding governing equations are derived and then solved by Laplace transform method and its numerical inversion. The distributions of the non-dimensional transverse deflection, temperature and displacement are obtained and illustrated graphically. In calculation, the influences of the ramp heating time parameter, the material length parameter, the nonlocal parameter, the time-delay factor and the kernel functions on the considered physical quantities are examined and discussed in detail.

Analysis and optimization of thermoelastic structures with tension–compression asymmetry

Many engineering and biological materials have been found to have tension–compression asymmetry properties. An extension of the linear thermoelastic behavior called a bi-modulus constitutive model is proposed to study the impact of thermo-mechanical coupling in such materials and structures. The well-posedness of the corresponding bi-modulus thermoelasticity problems is confirmed via a variational approach. An efficient numerical analysis method is developed for such nontrivial material behavior and is further employed for structural topology optimization. The importance of the proposed analysis and design framework is demonstrated by the significant impact of the tension–compression asymmetry and thermal effect on structural responses and optimum structural configurations.

The analysis and computation on nonlocal thermoelastic problems of blend composites via enriched second-order multi-scale computational method

This paper proposes an innovative enriched second-order multi-scale (SOMS) computational method to simulate and analyze the nonlocal thermoelastic problems of blend composites with stress and heat flux gradient behaviors. The multiple periodical heterogeneities and periodic configurations of investigated blend composites in different substructures result in a huge computational cost for direct numerical simulations. The significant characteristics of this study are as follows. (1) The nonlocal properties of blend composites in constitutive equations are converted into the source terms of thermoelastic balance equations. The novel macro-micro coupled SOMS computational model for these transformed nonlocal multi-scale problems is derived on the basis of multi-scale asymptotic analysis. The nonlocal thermoelastic behaviors of blend composites can be merely uncovered in the enriched SOMS solutions. (2) The error analysis in the pointwise sense is presented to elucidate the importance and necessity of establishing the enriched SOMS solutions. Furthermore, an explicit error estimate for the SOMS approximate solutions is obtained in the integral sense for these nonlocal multi-scale problems. (3) A multi-scale numerical algorithm is presented to effectively simulate nonlocal thermoelastic problems of blend composites based on finite element method (FEM). Finally, the capability of the proposed enriched SOMS computational method is demonstrated by typical two-dimensional (2D) and three-dimensional (3D) blend composites, presenting not only the excellent numerical accuracy but also the less computational cost. This work proposes a unified multi-scale computational framework for enabling nonlocal thermoelastic behavior analysis of blend composites.

Quantitative relationships between the mineral composition and macro mechanical behaviors of granite under different temperatures: Insights from mesostructure-based DEM investigations

Since the nuclear waste releases heat during the decay process, the mechanical behaviors of granites adjacent to the nuclear waste repository are inevitably impacted by the discrepancies in the thermal expansion characteristics of composite minerals. In this study, a mesostructure-based model (MSBM) was first proposed to characterize the thermal behaviors of varying minerals and cementation interfaces with consideration of the aperture-dependent weakening effects of pre-existing micro-cracks on mineral properties. Based on the MSBM, nine sets of numerical models with different mineral compositions were generated to explore the relationship between the mineral composition and the macro mechanical behaviors of granite at the temperatures of 25–250 °C. The meso-mechanisms behind the varied macro mechanical behaviors were comprehensively analyzed. The results indicate that the macro mechanical properties, i.e., the uniaxial compressive stress (UCS) and elastic modulus (E) are dependent on the combined effects of the different thermal expansion characteristics of minerals and the different thermoelastic behaviors of the crystalline interfaces, especially the quartz-biotite and quartz-feldspar mineral boundaries. Finally, an evaluation system aiming to quantify the effects of mineral composition and temperature on the mechanical behaviors of granite was proposed. Principal minerals such as quartz and feldspar strongly influence the UCS and E of the rock at different temperatures, and the influence of feldspar on UCS becomes more pronounced with increasing the temperature. Biotite has little influence on the change in elastic modulus with temperature, while the contribution of biotite to UCS varies with the temperature.

A deep learning approach based on the physics-informed neural networks for Gaussian thermal shock-induced thermoelastic wave propagation analysis in a thick hollow cylinder with energy dissipation

This paper proposes a novel approach based on the physics-informed neural networks (PINNs) as an efficient deep learning approach to solve a broad range of the coupled partial differential equations (PDEs). For the first time, the PINN methodology is successfully applied to the thermoelastic wave propagation analysis with energy dissipation in a thick hollow cylinder based on the Green-Naghdi (GN) theory of coupled thermoelasticity. The assumed thick hollow cylinder is subjected to Gaussian thermal shock loading applied on the inner bounding surface. This research presents a PINN architecture with self-adaptive weights, which does not suffer from the curse of dimensionality as opposed to the numerical methods. An in-depth discussion is provided on the method and its capabilities to address PDE-related issues. Moreover, the PINN-based parametric studies are performed to show the effects of the materials coefficients on the thermoelastic wave propagation and dynamic behaviors of the fields’ variables. Numerous examples of thermoelastic wave propagation analysis with and without energy dissipation are solved via this approach. The framework generates satisfactory results in terms of accuracy and stability, as summarized in the paper.

Thermodynamic behavior of Na-majorite and knorringite-majorite garnet systems

The behavior of thermal parameters pressure (P) and thermoelastic parameters i.e. Isothermal bulk modulus (K_T), its pressure derivative (K'T) and Thermal expansivity (α) has been analyzed for Na-majorite and knorringite-majorite systems at different compressions down to a maximum value of 0.3 for temperature ranges from 300 K to 1500 K. The pressure dependent compressibility of these garnets have been studied. The comprehensive study of thermodynamic and thermoelastic behavior at different isotherms and isobars respectively has been achieved by employing both Vinet equation of state and Anderson-Isaak equation. The study of thermal expansivity (α) using Anderson-Isaak and Stacy-Davis approach shows a similar trend of MgO system. Based on the validation of Kumar's approach, the lattice parameter of garnet system is computed using Kumar and modified Kumar's approach at high temperature and is found to be very less deviated from the value of lattice parameter at room temperature.

Thermoelastic wave propagation damping in a hollow FG-GPLRC cylinder with the spinning motion

This analysis deals with generalized thermoelasticity via Lord–Shulman’s theory for hollow cylinders reinforced with graphene platelets (GPL). The viscosity effect is also considered for applied materials. The second-order correlation homogenization techniques are utilized to obtain the equivalent thermo-mechanical properties. The hollow cylinder with spinning motion is modeled based on the linear thermoelastic constitutive law. The GPLs are functionally distributed along the cylinder’s radius based upon a power-law function. The Kelvin–Voigt type of viscosity behavior which is a differential state of viscous materials, is employed. The energy equation is attained based on the coupled and generalized framework. After obtaining the motion and energy equations in dimensionless form, the generalized differential quadrature (GDQ) and Newmark time marching methods are implemented to extract the temporal evolution and wave propagation of temperature, displacement, and stresses that occurred in the structure. After validating the responses with the available theoretical article, some numerical results are demonstrated to examine the effect of thermo-mechanical properties on the thermoelastic behavior of chosen nanocomposite cylinder.

Investigation of Nonlinear Thermo-Elastic Behavior of Fluid Conveying Piezoelectric Microtube Reinforced by Functionally Distributed Carbon Nanotubes on Viscoelastic-Hetenyi Foundation

In this paper, nonlinear and nonlocal thermo-elastic behavior of a microtube reinforced by Functionally Distributed Carbon Nanotubes, with internal and external piezoelectric layers, in the presence of nonlinear viscoelastic-Hetenyi foundation, and axial fluid flow inside the microtube is studied. Nonlinear partial differential equations governing the system are derived using Reddy’s third-order shear deformations theory along with the Von-Karman theory including the effect of fluid viscosity. Then, the equations are converted to time-dependent ordinary nonlinear equations using the Galerkin method. Afterward, the governing equations of the microtube’s lateral displacements are solved using the multiple scales method. The analysis of the piezoelectric’s parametric resonance is performed by obtaining trivial and nontrivial stationary solutions and plotting characteristic curves of the frequency response and voltage response. At the end, the effect of different parameters including the flow velocity, excitation voltage, parameters of the foundation, viscosity parameter, thermal loading and nanotubes’ volume fraction index on the nonlinear behavior of the system, under parametric resonance condition, is investigated.

Domain-independent thermoelastic coupling mechanism for multi-physical systems applications: a Bond Graph approach

In this paper, we propose a domain-independent nonlinear thermoelastic coupling element to enable the realization of a two-way dynamic coupling between the thermal and elastic domains. The implementation of the proposed coupling element in multi-physical systems modeling will provide reversibly conserved power transactions among the existing physical domains (thermal and elastic domains), which is a favorable demand in coupled field dynamic investigations. To guarantee a conserved and continuous power transmission between the thermal and elastic domains, by means of the Bond Graph notation, a reversible multi-dimensional storage element is designed, and the corresponding multi-dimensional constitutive equations are derived that satisfy the Maxwell reciprocity. The power network of each domain of interest is, also, represented in the Bond Graph notation, and the corresponding governing equation of each domain is extracted on the basis of physical system theory. The reversible connectivity of the thermal and elastic domains is then executed via replacing the storage elements of each of the domains with the proposed coupling element. The ensuing model will provide the thermoelastic behavior of the system from the reversible thermal and elastic domains’ energetic interactions, which preserves the fundamental physical natures of such phenomena in the model. The generated coupling element will allow the model of each physical domain to remain independent from other existing domains while they are dynamically coupled, which provides a unique benefit for multi-physical phenomena investigations.

Influences of Boundary Temperature and Angular Velocity on Thermo-Elastic Characteristics of a Functionally Graded Circular Disk Subjected to Contact Forces

The behaviors of functionally graded (FG) engineering structures are influenced by various parameters, such as the boundary temperature, the angular velocity, variations in the thickness, the weight of the structure, and the loading state. The thermo-elastic characteristics of FG rotating circular disks under the loading of contact forces were investigated. Hooke’s law in plane stress problems was applied to derive a pair of partial differential equations and a finite volume method was developed due to the complexity of the governing equations. The thermo-elastic characteristics of the FG rotating disks were investigated according to the variations in their outer boundary temperature and angular velocity. The increase in the outer boundary temperature caused crack generation at the inner surface of the circular disk and on the opposite side to the loading point. The increase in the angular velocity caused unstable thermo-elastic behaviors near the area of the outer boundary surface, especially at 0.7<(r−a)/(b−a) < 0.9, and may have led to crack generation at the outer surface of the rotating disk. These results may be applied to the design of functionally graded circular cutters or grinding disks undergoing contact forces to produce proper and reliable thermo-elastic characteristics for practical applications.

Ab initio simulations of α- and β-ammonium carbamate (NH4·NH2CO2), and the thermal expansivity of deuterated α-ammonium carbamate from 4.2 to 180 K by neutron powder diffraction.

Experimental and computational studies of ammonium carbamate have been carried out, with the objective of studying the elastic anisotropy of the framework manifested in (i) the thermal expansion and (ii) the compressibility; furthermore, the relative thermodynamic stability of the two known polymorphs has been evaluated computationally. Using high-resolution neutron powder diffraction data, the crystal structure of α-ammonium carbamate (ND4·ND2CO2) has been refined [space group Pbca, Z = 8, with a = 17.05189 (15), b = 6.43531 (7), c = 6.68093 (7) Å and V = 733.126 (9) Å3 at 4.2 K] and the thermal expansivity of α-ammonium carbamate has been measured over the temperature range 4.2-180 K. The expansivity shows a high degree of anisotropy, with the b axis most expandable. The ab initio computational studies were carried out on the α- and β-polymorphs of ammonium carbamate using density functional theory. Fitting equations of state to the P(V) points of the simulations (run athermally) gave the following values: V0 = 744 (2) Å3 and bulk modulus K0 = 16.5 (4) GPa for the α-polymorph, and V0 = 713.6 (5) Å3 and K0 = 24.4 (4) GPa for the β-polymorph. The simulations show good agreement with the thermoelastic behaviour of α-ammonium carbamate. Both phases show a high-degree of anisotropy; in particular, α-ammonium carbamate shows unusual compressive behaviour, being determined to have negative linear compressibility (NLC) along its a axis above 5 GPa. The thermodynamically stable phase at ambient pressure is the α-polymorph, with a calculated enthalpy difference with respect to the β-polymorph of 0.399 kJ mol-1; a transition to the β-polymorph could occur at ∼0.4 GPa.

Analysis of shock waves in a mixture theory of a thermoelastic solid and fluid with distinct temperatures

The continuum theory of mixtures is used to describe a medium consisting of a solid phase and fluid phase, both compressible and attributed distinct deformation, temperature, entropy, and internal energy fields. Continuum balance laws are presented, and constitutive equations consistent with thermodynamic restrictions are postulated. Jump conditions for shock waves are established. Evolution equations for transient, i.e., unsteady, shock wave propagation are newly derived for an ideal mixture consisting of an arbitrary number of nonlinear thermoelastic solids, whereby inviscid thermoelastic fluid behavior is attained for a given constituent under more restrictive constitutive assumptions. Detailed calculations of Hugoniot response and shock decay are specialized to the case of a two-phase mixture of a single solid and a single fluid, where physical properties pertinent to lung parenchymal tissue containing air are assigned. Local constitutive behaviors for this lung mixture model correspond to a compressible neo-Hookean solid phase and an ideal gas fluid phase. Predictions of the model offer new information on origins of soft tissue trauma, in the context of prior experimental observations, for dynamic impact or shock loading of the lung.

Thermo-elastic behavior of hexagonal Sc–Ti–Zr–Hf high-entropy alloys

Recent advances in tuning the long-standing strength-ductility tradeoff have drawn attention to high-entropy alloys (HEAs), and the appearance of hexagonal close-packed (hcp) structures has been emphasized. However, few studies have explored the elastic moduli of hcp HEAs, which is of prime importance for improved understanding of the outstanding mechanical properties. In this work, we focus on a set of equiatomic rare-earth-free HEAs with hcp structures, i.e. ScTiZr, ScTiHf, ScZrHf, TiZrHf, and ScTiZrHf, and their thermo-elastic properties are studied using quantum mechanical first-principles methods. It is found that, for all considered HEAs, the hexagonal axial ratio shows a weak dependence on the temperature effect, and the thermal expansion coefficient remains almost unchanged above room temperature. From the calculated temperature-dependent single-crystal elastic constants, we analyzed the mechanical stability, elastic anisotropy, and derived polycrystalline moduli. Results indicate that the present HEAs exhibit rather high elastic isotropy and large elastic softening resistance. The ab initio predicted Young’s modulus, shear modulus, and specific modulus do not obey the rule of mixture, which indicates that there exists a strong intrinsic hardening effect in all of the considered HEAs. The calculated results are in good agreement with the available experimental measurements.

Photo-thermoelastic behavior of a functionally graded? Semiconductor medium excited by thermal laser pulses

This work presents an analytical approach to study the photothermal response of a functionally graded semiconducting thermoelastic half-space. The generalized thermoelastic heat conduction theory without energy dissipation is employed to extract the governing equations in which the properties of a half-space material are supposed to change in the longitudinal direction. In the context of photothermal transitional model, the interaction between heat-elastic plasma waves is described. The governing equations for the physical field variables are determined by Laplace transform procedure in the physical domain. The distribution of each field variable as well as the spread of thermo-elastic-plasma waves are plotted and discussed. Some illustrative examples are presented to determine the influence of characteristic parameters such as thermal relaxation and the power law (nonhomogeneity) index on the thermoelastic behavior of the considered medium. Finally, some interesting situations are derived from the current formulation.

Thermoelastic Behavior of an Infinitely Long Cylindrical Shell Compliant to Shear under The Action Of Heat Sources Of Variable Power

Thermoelastic Behavior of an Infinitely Long Cylindrical Shell Compliant to Shear under The Action Of Heat Sources Of Variable Power

Finite element model for a coupled thermo-mechanical system in nonlinear strain-limiting thermoelastic body

We investigate a specific finite element model to study the thermoelastic behavior within the context of nonlinear strain-limiting constitutive relation. As a special subclass of implicit relations, the thermoelastic response of our interest is such that stresses can be arbitrarily large but strains remain small, particularly in the neighborhood of crack-tips. In the present communication, we consider a two-dimensional coupled system — linear and quasi-linear partial differential equations for temperature and displacements, respectively. A standard finite element method of continuous Galerkin is then employed to obtain the numerical solutions for the field variables, where two distinct temperature distribution of the Dirichlet type are considered for boundary condition. From a domain with an edge-crack, we find that the near-tip strain growth in the proposed model is slower than the growth of stress, which is the salient feature compared to the predictions of singular strain based on the classical linearized description of the elastic body. In essence, the model can be inherently consistent with the assumption of linearized elasticity and infinitesimal strain theory. This study can provide a theoretical and computational framework to develop physically meaningful models and examine other coupled multi-physics such as an evolution of complex network of cracks induced by thermal shocks.

On size-dependent generalized thermoelasticity of nanobeams

In this article, a size-dependent generalized thermoelasticity model is established to appraise the small-scale effect on thermoelastic vibrations of Euler-Bernoulli nanobeams. Small-scale effect on the structure and heat conduction is captured by exploiting nonlocal strain gradient theory (NSGT) and nonclassical heat conduction model of Guyer and Krumhansl (GK model). NSGT enables the model to account for both nonlocal and strain gradient effects on structure, and GK formulation empowers the model to incorporate both nonlocal and lagging effect into heat conduction equation. The normalized forms of size-dependent equations of motion and heat conduction are provided by introducing some dimensionless parameters. This system of normalized differential equations is then solved with the aid of the Laplace transform to determine thermoelastic responses of nanobeams. Through various examples, a complete parametric study is conducted to clarify the pivotal role of nonclassical scale parameters in thermoelastic behavior of nanobeams. Comparing the results extracted based on various relative magnitudes of nonlocal and strain gradient length scale parameters implies that NSGT is capable of expounding both hardening and softening phenomenon in nanoscale structures. The outcomes also reveal that GK model anticipates less energy dissipation.

Finite element analysis of thermoelastic free vibration behaviour of hardcore higher-order doubly curved sandwich shell panel

Finite element analysis of thermoelastic free vibration behaviour of hardcore higher-order doubly curved sandwich shell panel

Thermal vibration in rotating nanobeams with temperature-dependent due to exposure to laser irradiation

<abstract> <p>Effective classical representations of heterogeneous systems fail to have an effect on the overall response of components on the spatial scale of heterogeneity. This effect may be critical if the effective continuum subjects' scale differs from the material's microstructure scale and then leads to size-dependent effects and other deviations from conventional theories. This paper is concerned with the thermoelastic behavior of rotating nanoscale beams subjected to thermal loading under mechanical thermal loads based on the non-local strain gradient theory (NSGT). Also, a new mathematical model and governing equations were constructed within the framework of the extended thermoelastic theory with phase delay (DPL) and the Euler-Bernoulli beam theory. In contrast to many problems, it was taken into account that the thermal conductivity and specific heat of the material are variable and linearly dependent on temperature change. A specific operator has been entered to convert the nonlinear heat equation into a linear one. Using the Laplace transform method, the considered problem is solved and the expressions of the studied field variables are obtained. The numerical findings demonstrate that a variety of variables, such as temperature change, Coriolis force due to rotation, angular velocity, material properties, and nonlocal length scale parameters, have a significant influence on the mechanical and thermal waves.</p> </abstract>

A visual and full-field method for detecting quench and normal zone propagation in HTS tapes

A fast and effective quench detection method is especially challenging in the development of high-field high-temperature superconducting (HTS) magnets for their safe operations and reliably releasing the stored energy during a quench. The occurrence and propagation of a quench are often accompanied by strong thermal and magneto-mechanical responses within superconducting magnets. Aiming to detect a quench in the whole process and capture the thermoelastic behavior associated with it, a new detection technique with a visual and full-field perception based on the digital image correlation (DIC) method is proposed in the present study. The experiment of a quench triggered thermally by a local spot heater is conducted for a YBCO coated conductor tape in a cryogenic chamber. The evolution and characteristics of the full-field strain in the HTS tape during the processes of a non-quench, a quench occurrence and quench propagation are intuitively presented with experimental observations. For the comparison purpose, the conventional quench detection methods by monitoring temperature and voltage signals during a quench are also utilized experimentally. The results verify the visual and full-field quench detection method, which uses a criterion of thermoelastic strain-rate for the quench occurrence and the evolution of strain contours for the normal zone propagating aspect. Additionally, a numerical quench model of coupled thermoelasticity to simulate the experiment is established and solved with the aid of Comsol multiphysics software. The quantitative results are in good agreement with the experimental measurements to prove the reliability and availability of the developed detection method. Since the DIC method is non-contact and insensitive to intense electromagnetic interferences, it is expected to provide a new technique on quench issues and some basic measurements on strain/stress behaviors in extreme environments of high-field HTS magnets in the future.