The homogenized dynamical model of a thermoelastic composite stitched with reinforcing filaments.

The dynamical problem of linear thermoelasticity for a body with incorporated thin rectilinear inclusions is studied. It is assumed that the inclusions (i.e. filaments and threads) are parallel to each other and the problem contains a small parameter [Formula: see text], which characterizes the distance between two neighbouring inclusions. Using the two-scale convergence approach, we find the limiting problem as [Formula: see text]. As a result, we get a well-posed homogenized model of an anisotropic inhomogeneous body with effective characteristics inheriting thermomechanical properties of inclusions.This article is part of the theme issue 'Non-smooth variational problems with applications in mechanics'.

Measurement of Nanometer Distances in Solution via 13 C NMR Spectroscopy-Shrinking of Macrocycles with Increasing Temperature.

For a molecular system, size and shape are of elementary importance for its function and properties. Therefore, the determination of distances within a molecule is essential. However, the commonly used methods are only suitable for distances smaller than 4 Šor larger than 15 Å. Here, we show that by incorporating a molecular spring, we can measure distances in macrocycles in the range of 10 Šusing 13 C NMR spectroscopy. The accuracy of the method also allows to determine the temperature dependence of the distances. In one case, we find a contraction of the length by almost 10 % upon heating. This shrinking due to heating can be considered as inverse thermoelasticity at the molecular level and is a previously completely overlooked phenomenon that can be used in the future as a tool to change the length and, thus, the function of a system.

Energy/entropy partition of force at DNA stretching.

We compute by molecular simulation the energy/entropic partition of the force in a stretched double-stranded (ds)DNA molecule that is not yet available from the single-molecule measurements. Simulation using the coarse-grained wormlike chain (WLC) model predicts a gradual decrease in the internal (bending) energy of DNA at stretching. The ensuing negative energy contribution to force fU is outweighed by the positive entropy contribution fS . The ratio fU /f, used to assess the polymer elasticity, is about -1 at the moderate extension of DNA. At the high extension, the extra energy expenses due to the contour length elongation make the ratio fU /f less negative. The simulation findings of the hybrid energy/entropy nature of DNA elasticity at weak and moderate forces are supported by computations using the thermoelastic method mimicking the polymer experiments in bulk. It is contended that the observation of the negative energy elasticity in DNA can be generalized to other semiflexible polymers described by the WLC model.

Multiscale analysis of stationary thermoelastic vibrations of a composite material.

The problem of description of stationary vibrations is studied for a planar thermoelastic body incorporating thin inclusions. This problem contains two small positive parameters [Formula: see text] and [Formula: see text], which describe the thickness of an individual inclusion and the distance between two neighbouring inclusions, respectively. Relying on the variational formulation of the problem, by means of the modern methods of asymptotic analysis, we investigate the behaviour of solutions as [Formula: see text] and [Formula: see text] tend to zero. As the result, we construct two models corresponding to the limit cases. At first, as [Formula: see text], by the version of the method of formal asymptotic expansions we derive a limit model in which inclusions are thin (of zero width). Then, from this limit model, as [Formula: see text], we derive a homogenized model, which describes effective behaviour on the macroscopic scale, i.e. on the scale where there is no need to take into account each individual inclusion. The limiting passage as [Formula: see text] is based on the use of the two-scale convergence theory. This article is part of the theme issue 'Non-smooth variational problems and applications'.

Continuum Thermodynamics of Constrained Reactive Mixtures.

Mixture theory models continua consisting of multiple constituents with independent motions. In constrained mixtures, all constituents share the same velocity but they may have different reference configurations. The theory of constrained reactive mixtures was formulated to analyze growth and remodeling in living biological tissues. It can also reproduce and extend classical frameworks of damage mechanics and viscoelasticity under isothermal conditions, when modeling bonds that can break and reform. This study focuses on establishing the thermodynamic foundations of constrained reactive mixtures under more general conditions, for arbitrary reactive processes where temperature varies in time and space. By incorporating general expressions for reaction kinetics, it is shown that the residual dissipation statement of the Clausius-Duhem inequality must include a reactive power density, while the axiom of energy balance must include a reactive heat supply density. Both of these functions are proportional to the molar production rate of a reaction, and they depend on the chemical potentials of the mixture constituents. We present novel formulas for the classical thermodynamic concepts of energy of formation and heat of reaction, making it possible to evaluate the heat supply generated by reactive processes from the knowledge of the specific free energy of mixture constituents as well as the reaction rate. We illustrate these novel concepts with mixtures of ideal gases, and isothermal reactive damage mechanics and viscoelasticity, as well as reactive thermoelasticity. This framework facilitates the analysis of reactive tissue biomechanics and physiological and biomedical engineering processes where temperature variations cannot be neglected.

Thermoelastic behavior of skin tissue induced by laser irradiation based on the generalized dual-phase lag model.

This paper analyzes the thermoelastic responses of skin tissue during laser irradiation based on a generalized dual-phase-lag (DPL) model. The method of separation of variables is utilized to obtain the analytical solutions for thermal and mechanical responses. The influences of some crucial parameters on temperature, displacement and stress evolutions are discussed, including the phase lag of heat flux, the phase lag of temperature gradient and the phase lag of laser pulse, the coupling factor between tissue and blood, the porosity of tissue, the equivalent diameter of tissue and the diameter of blood vessels. The generalized DPL bio-heat transfer model predicts different results from those by the classical DPL model and Pennes model. The equivalent diameter of tissue affects the coupling factor between tissue and blood, while the diameter of blood vessels mainly affects the porosity of tissue.

An External Circular Crack in an Infinite Solid under Axisymmetric Heat Flux Loading in the Framework of Fractional Thermoelasticity.

In a real solid there are different types of defects. During sudden cooling, near cracks, there can appear high thermal stresses. In this paper, the time-fractional heat conduction equation is studied in an infinite space with an external circular crack with the interior radius R in the case of axial symmetry. The surfaces of a crack are exposed to the constant heat flux loading in a circular ring R

Fractional thermoelasticity problem for an infinite solid with a penny-shaped crack under prescribed heat flux across its surfaces.

The time-nonlocal generalization of the Fourier law with the 'long-tail' power kernel can be interpreted in terms of fractional calculus and leads to the time-fractional heat conduction equation with the Caputo derivative. The theory of thermal stresses based on this equation was proposed by the first author (J. Therm. Stresses 28, 83-102, 2005 (doi:10.1080/014957390523741)). In the present paper, the fractional heat conduction equation is solved for an infinite solid with a penny-shaped crack in the case of axial symmetry under the prescribed heat flux loading at its surfaces. The Laplace, Hankel and cos-Fourier integral transforms are used. The solution for temperature is obtained in the form of integral with integrands being the generalized Mittag-Leffler function in two parameters. The associated thermoelasticity problem is solved using the displacement potential and Love's biharmonic function. To calculate the additional stress field which allows satisfying the boundary conditions at the crack surfaces, the dual integral equation is solved. The thermal stress field is calculated, and the stress intensity factor is presented for different values of the order of the Caputo time-fractional derivative. A graphical representation of numerical results is given. This article is part of the theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives'.

A thermo-mechanically loaded rotating FGM cylindrical pressure vessels under parabolic changing properties: An analytical and numerical analysis.

This study aims to develop an exact analytical solution for steady-state thermo-mechanical stress in a functionally graded (FG) thick-walled cylindrical vessel. The cylinder is subjected to combined rotational speed and internal pressures while the thermal load is with convective and radiative boundary conditions. The dimensionless governing equations and boundary conditions, represented as a quartic equation, are derived and solved using Ferrari's method. The temperature, displacement, and stress fields across the thick-walled cylindrical vessel are calculated by finding the roots of the quartic equation. In order to investigate the accuracy of the exact analytical solution, a numerical model is constructed based on a standard Galerkin discretization approach of the finite element method (FEM). The analytical solutions and the results obtained through FEM show a high level of agreement. Furthermore, the study analyzes the effects of material parameters on temperature, displacement, and stress fields. Displacement, temperature, and stress fields are presented in the form of dimensionless graphs along the radial direction. For the considered parametric studies, results revealed that parabolic grading is beneficial than conventional grading. This study reveals that for the thermal loading, the maximum temperature, displacement, and tangential stress decrease for the parabolic grading. A similar but lower value of temperature, displacement, and tangential stress is also observed in the case of thermomechanical loading. This study is expected to assist in the assessment of the reliability of load calculations and contribute to the overall durability of pressure vessels. The results obtained from this study can provide valuable insights into thermo-elasticity and the thermo-mechanical behavior of thick-walled cylindrical vessels and can aid in the design and optimization of such systems.

Finite-Element Modeling of the Temperature Effect on Extended Avalanche Damage of Gas Main Pipelines.

The dynamic stress-strain state and fracture of a steel main gas pipe section between supports with a straight-through crack was analyzed with consideration of the temperature effect on changes in the mechanical properties of the pipe material. The numerical solution of the problem was implemented in the ANSYS-19.2/Explicit Dynamics software package. The process of fracture in a section of the gas pipeline "Beineu-Bozoy-Shymkent" with a linear crack in the temperature range of -40 °C to +50 °C at the operating pressure of 7.5 MPa and critical pressure equal to 9.8 MPa was considered. As a result, it was found that at the initial growth of the internal pressure from working pressure to critical pressure, the length of the crack doubled. At the same time, the process had a local characteristic. Further development of the crack had the nature of avalanche fracture and depended on the temperature of the steel pipeline. With increasing temperature, there was also an increase in the length of the crack at the avalanche fracture. Thus, at a temperature of 40 °C, the crack lengthened 67.75-fold; at a temperature of -10 °C, the crack lengthened 68-fold; at a temperature of +20 °C, the crack lengthened 68.25-fold; and at a temperature of +50 °C, the crack lengthened 68.5-fold. In this work, this difference was 75% of the initial crack length. This fact will be used for further development of the technique of strengthening damaged pipe sections using bandages.

Finite element analysis of a generalized rotating FGM vessel subjected to thermo-mechanical loadings: Effect of Poisson ratio and inhomogeneity parameters.

Cylinders and thick walled cylindrical shells are commonly utilized in several industries to transport and store fluids under certain pressure and temperature conditions. In the present paper, a numerical solution is developed in order to investigate displacement, temperature and stress fields in a rotating pressure vessel made of generalized functionally graded material (FGM) subjected to different thermo-mechanical boundary conditions. The aim is to investigate the effect of Poisson ratio, internal pressure and temperature and inhomogeneity parameters on the stress and deformation distributions of the rotating pressure vessel. The material is considered isotropic nonhomogeneous and linearly elastic with its properties varying along the radial direction. Additionally, certain conditions, such as exterior or interior problems where r → ∞ or r → 0, respectively, are impossible to resolve using the variation of attributes as a power-law distribution. An approach to the spatial Young modulus distribution that is more broad has been suggested in the literature which can be applied to such physical challenges. The rotation of the pressure vessel is considered in the analysis, and the temperature distribution is assumed to be non-uniform. Since an analytical solution to the differential equation is not accessible, the conventional Galerkin discretization approach of the Finite Element Method (FEM) is applied, nowadays is considered one of the main numerical tools for solving Boundary Value Problems (BVP). It is addressed how stress, strain, and displacement are affected by the inhomogeneity parameter, rotation speed, pressure, temperature, and Poisson ratio. The examination of the various findings indicates that changes in the temperature profile, rotation, and inhomogeneity parameter on the thermoelastic field have a substantial impact on the stress and strain in the FGM cylinder. The findings indicate that the Poisson ratio and inhomogeneity parameters have a significant impact on the stress and deformation distributions. According to the results, the above-mentioned parameters can be adapted to control the thermoelastic filed in a FGM cylinder. The present research offers significant perspectives on the development and enhancement of rotating FGM pressure vessels intended for high-temperature applications.

Parametric Analysis of Thick FGM Plates Based on 3D Thermo-Elasticity Theory: A Proper Generalized Decomposition Approach.

In the present work, the general and well-known model reduction technique, PGD (Proper Generalized Decomposition), is used for parametric analysis of thermo-elasticity of FGMs (Functionally Graded Materials). The FGMs have important applications in space technologies, especially when a part undergoes an extreme thermal environment. In the present work, material gradation is considered in one, two and three directions, and 3D heat transfer and theory of elasticity equations are solved to have an accurate temperature field and be able to consider all shear deformations. A parametric analysis of FGM materials is especially useful in material design and optimization. In the PGD technique, the field variables are separated to a set of univariate functions, and the high-dimensional governing equations reduce to a set of one-dimensional problems. Due to the curse of dimensionality, solving a high-dimensional parametric problem is considerably more computationally intensive than solving a set of one-dimensional problems. Therefore, the PGD makes it possible to handle high-dimensional problems efficiently. In the present work, some sample examples in 4D and 5D computational spaces are solved, and the results are presented.

Blunt head impact causes a temperature rise in the brain.

A magnetic resonance imaging-based finite-element model is employed to assess the temperature in the human brain due to blunt head trauma. The model is based on a coupled thermoelasticity under small strain and Fourier or Maxwell-Cattaneo heat conduction assumptions, accompanied by a standard coupling of thermal fields to mechanics. It is found that mechanical impacts on the forehead cause a temperature rise of up to 0.3°C above the reference homogeneous temperature field.

Effect of Heating Conditions during Moulding on Residual Stress-Strain Behaviour of a Composite Panel.

Currently, we observe extensive use of products made of polymeric composite materials in various industries. These materials are being increasingly used to manufacture large-sized structural parts that bear significant loads. However, increase in the volume of composites used in critical structures is impeded by the instability of properties of the resulting products. In most cases, the reason for this is the residual thermal stress-strain behaviour of the composite structure. This paper deals with the development of a method to predict the residual stress-strain behaviour depending on the heating conditions and distribution of the temperature field over the thickness of the moulded composite package. The method establishes the relationship between moulding process parameters and the effect of the auxiliary and basic equipment on the distribution of the temperature field, stresses, and strains in the moulded product. It is shown that the rate of temperature change at the stage of heating has its effect on the amount of residual deformation of the structure. Experimental studies have been carried out to determine the influence of several factors (rates of heating and cooling) on the residual deflection of the composite panel. Experimental data proves that specimens moulded under conditions of an increased heating rate get a greater deflection than those moulded at a lower heating rate. The error of results during the full-scale experiment did not exceed 6.8%. Our results provide an opportunity to determine the residual thermal stress-strain behaviour of the moulded structure with the required degree of accuracy without a series of experiments. It allows us to significantly simplify the practical implementation of the developed method and avoid any additional production costs.

Determination of the Composite Panel Moulding Pressure Value.

Currently, prefabricated panel structures are typical products made of polymeric composite materials. The integrity of the composite panels, their structure and accuracy of making a contour are largely associated with the manifestation of residual technological stresses. The above phenomena and associated stress-strain behaviour inevitably occur in the process of moulding of the composite products. However, their value, nature, time of occurrence and dynamics of growth can be fully controlled and regulated. The paper deals with the study of the effect of moulding pressure on the quality of a composite product. A dependence is presented that allows us to determine the time for the degassing of the polymeric composite material package at the given temperature and pressure to obtain a monolithic and nonporous structure. It is shown that the peak of the maximum volatile-matter yield for the considered binder types lies in the temperature range where the degree of curing does not exceed 10%; that is, the viscosity values do not prevent the removal of volatile fractions. The effect of moulding pressure on the values of the volume content of the reinforcing material has been studied, and the dependence of the required thickness of the absorbent layer on the parameters of the package of polymer composite material and pressure has been obtained. The dependence of the required thickness of absorbent layer on the parameters of the package of polymeric composite material and pressure has been obtained. The mathematical model developed by us provides an opportunity to predict the stress-strain behaviour of a composite structure at any time during the moulding process. The model is closely related to chemo-viscous and thermal models. It allowed us to synthetize a method for choosing the rational parameters of the moulding process (temperature, pressure, and time), materials of additional layers and equipment. The experiments proved the presence of several defects, such as de-lamination of edges, waviness, swelling and poor adhesion of upper layers in the specimen of the composite panel cooled stepwise in the absence of the vacuum pressure. The surface quality of the specimen of the panel cooled stepwise under vacuum pressure was significantly better, and no visible defects were observed. The obtained theoretical values of deflections, considering the change in physic-mechanical characteristics that depend on the temperature and rheonomic properties of the material, showed an error that did not exceed 7%, compared to the experimental data. Our results can be applied at the enterprises engaged in designing and manufacturing panel structures of polymeric composite materials.

Boundary Element and Sensitivity Analysis of Anisotropic Thermoelastic Metal and Alloy Discs with Holes.

The main aim of this paper was to develop an advanced processing method for analyzing of anisotropic thermoelastic metal and alloy discs with holes. In the boundary element method (BEM), the heat impact is expressed as an additional volume integral in the corresponding boundary integral equation. Any attempt to integrate it directly will necessitate domain discretization, which will eliminate the BEM's most distinguishing feature of boundary discretization. This additional volume integral can be transformed into the boundary by using branch-cut redefinitions to avoid the use of additional line integrals. The numerical results obtained are presented graphically to show the effects of the transient and steady-state heat conduction on the quasi-static thermal stresses of isotropic, orthotropic, and anisotropic metal and alloy discs with holes. The validity of the proposed technique is examined for one-dimensional sensitivity, and excellent agreement with finite element method and experimental results is obtained.

Refined Lord-Shulman Theory for 1D Response of Skin Tissue under Ramp-Type Heat.

In this article, we present a mathematical model of thermoelastic skin tissue based on a refined Lord-Shulman heat conduction theory. A small thickness of skin tissue is considered to be one-dimensional with mechanical clamped surfaces. In addition, the skin tissue's outer surface is subjected to ramp-type heating while its inner surface is adiabatic. A simple Lord-Shulman theory, as well as the classical coupled thermoelasticity, are also applied in this article. Laplace transform techniques and their inversions are calculated to return to the time domain. Numerical outcomes are represented graphically to discuss the significant impacts on the temperature, dilatation, displacement, and stress distributions. Such results provide a more comprehensive and better insight for understanding the behavior of skin tissue during the temperature distribution of a specific boundary condition.

Phase Field Models for Thermal Fracturing and Their Variational Structures.

It is often observed that thermal stress enhances crack propagation in materials, and, conversely, crack propagation can contribute to temperature shifts in materials. In this study, we first consider the thermoelasticity model proposed by M. A. Biot and study its energy dissipation property. The Biot thermoelasticity model takes into account the following effects. Thermal expansion and contraction are caused by temperature changes, and, conversely, temperatures decrease in expanding areas but increase in contracting areas. In addition, we examine its thermomechanical properties through several numerical examples and observe that the stress near a singular point is enhanced by the thermoelastic effect. In the second part, we propose two crack propagation models under thermal stress by coupling a phase field model for crack propagation and the Biot thermoelasticity model and show their variational structures. In our numerical experiments, we investigate how thermal coupling affects the crack speed and shape. In particular, we observe that the lowest temperature appears near the crack tip, and the crack propagation is accelerated by the enhanced thermal stress.

Laser induced thermoelastic contributions from windows to signal background in a photoacoustic cell.

The existence of a signal baseline due to a variety of reasons in a photoacoustic (PA) gas measurement system is a common phenomenon. One major component is the absorption of optical windows in an enclosed PA cell. This work explores the relation between the background signal and the thermoelastic effect inside the windows by modelling the pressure and elastic wave field by means of a Green-function based method. The influence of laser incidence location, angle and radius is discussed based on a rigorous three-dimensional solid-to-fluid coupling model. The effects were theoretically demonstrated culminating in the determination of best (minimum background signal) performance using a collimated and expanded incident laser beam. The results were also validated through experiments.

Quasi-harmonic thermoelasticity of palladium, platinum, copper, and gold from first principles.

We calculate the temperature-dependent elastic constants (ECs) of palladium, platinum, copper and gold within the quasi-harmonic approximation using a first-principles approach and evaluating numerically the second derivatives of the Helmholtz free-energy with respect to strain at the minimum of the free-energy itself. We find an overall good agreement with the experimental data although the anomalies of palladium and platinum reported at room temperature are not reproduced. The contribution of electronic excitations is also investigated: we find that it is non-negligible for theC44ECs of palladium and platinum while it is irrelevant in the other cases. Its effect is not sufficient to explain the details of the anomalies found by experiments, not even when, in the case of platinum, we take into account the electron-phonon interaction. Lastly, the effect of the exchange and correlation functional is addressed and it is found that it is important atT= 0 K, while all functionals give similar temperature dependencies.