Simulating thermoelastic distortion in a body with internal degrees of freedom

Summary A system of equations has been formulated for a thermoelastic model for a body having internal degrees of freedom. The local thermodynamic state is put into correspondence with vector and tensor parameters in accordance with the extent of the structural change. A model problem of hardening in an isotropic layer is considered.Translated from Fiziko-khimicheskaya Mekhanika Materialov, Vol. 27, No. 3, pp. 79–83, May–June, 1991.     

3D elastodynamic fields of non-uniformly coated obstacles: Notion of eigenstress and eigenbody-force fields

Based on wave-function expansion, the time harmonic wave scattered by a circular and spherical inhomogeneity has been studied by numerous investigators. This method has also been employed to axisymmetrically coated circular and spherical inhomogeneities by some authors. When the geometry of the obstacle is not axisymmetric, the wave-function expansion is no longer applicable. In this paper, it is proposed to employ the dynamic equivalent inclusion method (DEIM) which is more general than the methods presented in the literature. It will be seen that DEIM may be used to treat a wide range of situations in a unified manner and is not bound to certain symmetries. The DEIM was first proposed by Fu and Mura [Fu, L.S., Mura, T., 1983. The determination of elastodynamic fields of an ellipsoidal inhomogeneity. ASME J. Appl. Mech. 50, 390–396], and no further developments have been done on it ever since. Its original formulation has some shortcomings with regard to the concept of homogenizing eigenstrains, and for usage of polynomial eigenstrains. Moreover, it is limited to single ellipsoidal inhomogeneity without coating. The new viewpoints of homogenizing eigenstress and eigenbody-force fields which are compatible with the physics of the problem are given. Expressing the eigenstress, eigenbody-force fields and the Green’s function associated with the governing Helmholtz equation in terms of the spherical wave-functions is the natural choice and is very effective. Another important task is the development of the three dimensional DEIM for inhomogeneities having homogeneous or functionally graded (FG) coating with variable thickness, which eliminates any possible symmetries.     

Design and optimization of a low-frequency electric field sensorusing Pockels effect

The present paper proposes an optical device for measuring low-frequency (50-60 Hz) high electric fields (0-200 kV.cm^-1) using a LiNbO₃ crystal as sensing medium without any contacting electrode. Thus, a good galvanic insulation of material and person is obtained. An experimental setup is developed in the laboratory by using the electro-optical effect or Pockels effect, and several measurements are realized. Simulations are performed with the finite element method (FEM) to optimize the sensing medium of the device. Experimental and simulation results are presented and discussed. The sensor induces a weak disturbance of the local electric field to be measured. The sensibility of the sensor is about 4 μA/(kV.cm^-1 )     

Josephson effect devices and low-frequency field sensing

Three major areas of application of the Josephson effect are recognized; absolute standards, millimetre and sub-millimetre wave sensing, and dc and low-frequency current, voltage, and magnetic field sensing. In the latter area, single junction rf-biased low-inductance loop devices in a number of different forms (junction types and loop geometries) have been developed with sensitivities of the order of 10⁻¹⁵ T (10⁻¹¹ G) or 10⁻¹⁹ V. These sensors are being used in applications as diverse as magnetocardiography and absolute noise thermometry in the millikelvin range. As amplifiers, they are characterized by demonstrated equivalent noise temperatures of less than a few millikelvin, and probably a few microkelvin (theoretical). Highly reliable thin-film loop devices in a number of different forms have been developed in several laboratories, but the more easily-made point-contact devices are probably the most widely used. Many of the characteristics of the devices can be easily interpreted with the aid of a pendulum analogue.     

基于热弹性耦合理论的功能梯度材料薄壁旋转碟片力学性能

基于热弹性耦合理论,对处于热载荷下的Al-Al₂O₃功能梯度材料（FGM）薄壁旋转碟片进行研究。根据FGM构造理论结合碟片轴对称特性,得到其力学特性全场分布。分别采用函数构造方法和热耦合传导方程推导得到模型所处温度场,并加以分析对比。建立了统一温度场的热耦合本构方程,并根据平面应力情况下热弹性材料力学特性基本原理,拟合确定其物性系数。通过微分求积方法（DQM）求解不同温度场下不同FGM构造形式模型的位移控制方程。结果表明:常温下,热耦合本构方程可以退化到胡克定律;经典热弹性理论与热弹性耦合理论下的碟片径向位移误差可达41.7%;热弹性耦合理论的结果随温度非线性变化,这种变化趋势也体现在大量科学实验中;碟片外表面温度变化、转速和所处的温度场显著地影响其热弹性场。      

Axisymmetric thermoelastic interactions in an unbounded body with cylindrical cavity

Summary Thermoelastic interactions in a linear, homogeneous and transversely isotropic unbounded body containing a cylindrical cavity due to a uniform step in stress or temperature applied to the boundary of the cavity are studied. A unified system of governing equations that includes among its particular cases the governing equations of the conventional and generalized thermoelasticity theories is employed. By the use of the Laplace transform technique, short time solutions for the temperature, displacement radial stress and hoop stress are constructed. The discontinuities suffered by these fields at the wavefronts are computed. Comparison with the corresponding results obtained in earlier works is made. Numerical results for a single crystal of zinc are presented.     

Functional grading of rubber tubes within the context of a molecularly inspired finite thermoelastic model

Summary. The concept of functional grading is applied to rubber-like materials within the framework of finite thermoelasticity. A phenomenological stress-strain relation is proposed to account for the finite chain extensibility, the entropic origin for the stress, as well as the graded nature of rubbers. As an application, the azimuthal shearing of a hollow rubber tube subjected to thermal loading is considered with a view toward minimizing the strain inhomogeneity, and an optimum grading for each temperature gradient is presented.     

Electrodynamics of superconductors. Response to a weak,low-frequency magnetic field

The phenomenon of the penetration of a low-frequency weak magnetic field into a superconductor has stimulated extensive theoretical and experimental studies. These have led to important clarifications regarding the nature of the superconducting phase by, for example, making concrete the idea of the long-range order in terms of the coherence length, which in turn has provided an understanding of the details of the penetration phenomenon under various conditions realized for different relative values of the penetration depth and the coherence length. This work is a review of the theoretical and experimental studies of the penetration phenomenon. The theory of the penetration phenomenon is discussed phenomenologically and microscopically. Different experimental techniques employed to study the phenomenon are discussed. Many of the experimental studies are concerned with the temperature dependence of the penetration depth. These results are reviewed for different elemental superconductors. Practical difficulties in a quantitative analysis of such data are pointed out. A new strategy adopted recently by Egloffet al. for analyzing the penetration depth data of pure lead is discussed. Effects of impurities, anisotropy of the Fermi surface, and the magnetic field on the penetration phenomenon are also discussed.     

Finite element analysis of the thermoelastic interactions in an unbounded body with a cavity

Thermoelastic interactions in an infinite homogeneous elastic medium with a spherical or cylindrical cavity are studied. The cavity surface is subjected to a ramp-type heating of its internal boundary which is assumed to be traction free. A general finite element model is proposed to analyze transient phenomena in thermoelastic solids. Lord–Shulman and Green–Lindsay for the generalized thermoelasticity model are selected for that purpose since it allows for “second sound” effects and reduces to the classical model by appropriate choice of the parameters. The problem has been solved numerically using a finite element method (FEM). Numerical results for the temperature distribution, displacement, radial stress and hoop stress are represented graphically. A comparison is made with the results predicted by the three theories.     

An elastodynamic fracture analysis in a centre-cracked plate

A two-dimensional linear elastodynamic analysis of crack initiation and fast crack propagation in a centre-cracked plate, subjected to constant tension is presented. The analysis is performed using the previously developed SMF2D code in its generation mode. The experimentally measured crack tip motion, as well as the specimen's geometry and its material characteristics serve as input to the simulation. The dynamic stress intensity factor, the dynamic energy release rate, and the various energy distributions are subsequently evaluated. Special attention is given to the influence of the energy supplied to the body during the fracture process due to the work done by the external tractions.     

The thermoelastic effect in PMMA

The thermoelastic effect has been measured in polymethylmethacrylate under both tensile and compressive uniaxial stress and the resulting temperature change for a known applied stress has been used to calculate the linear expansion coefficient of PMMA over a range of temperatures from 295 to 355 K and uniaxial stress in the elastic range using the Thompson relationship: Δθ= ? αTΔσ/ρC _p. Results are shown to agree with other measurements on the same material. An unexplained variation of α with stress has been observed at low values of applied stress. Values of the simple Grüneisen coefficient (γ_G) have been calculated over the same ranges of temperature and stress from the relationship: γ _G=3Δθ B _s /TΔσ.     

浅海低频声场的水平纵向相关性

基于一次浅海声学实验数据,研究了浅海低频声场的水平纵向相关特性。利用简正波干涉理论,对实验结果中声场水平纵向相关的振荡结构与强烈起伏现象进行了分析与解释。声场水平纵向相关的振荡结构是由简正波干涉所致,该实验结果进一步验证了该现象在浅海低频条件下的普遍性。当实验中采用的爆炸声源的标称深度位于声场中某号有效简正波的一个波节附近,声源实际爆炸深度的较小变化引起该号与其它号有效简正波幅度比值的较大变化,从而在有效简正波号数较少的情况下引起了声场水平纵向相关的强烈起伏现象,该现象表明在一定条件下声源深度是浅海低频声场水平纵向相关的一个敏感参数。     

The impact of a thermoelastic rod against a rigid heated barrier

The impact of a thermoelastic rod with a heat-insulated lateral surface against a rigid heated barrier is considered. The heat exchange between the rod and the wall occurs at one of its ends contacting with the wall, while the other end is heat-insulated and free from external forces. The behaviour of the rod during the impact process is described by the Green-Naghdy theory which allows one to take finite speed of heat propagation into account, neglecting therewith thermal relaxation. The Laplace integral transform with the subsequent expansion of the found images in terms of the natural functions of the problem is used as a method of solution, which is found in explicit exact closed form. The analytical time-dependence of displacements, stresses, and temperature at each rod particle is obtained. The emphasis is on the analysis of the contact stress, the temperature of the colliding bodies during their contact interaction, and on the detection of the duration of contact of the rod with the rigid wall. It is shown that the contact time essentially depends on the relationship between the mechanical and thermal values.     

Influence of a low-frequency acoustic field on the carillary impregnation of gas-saturated porous systems

Experimental results on the influence of a low-frequency acoustic field on the capillary impregnation of gas-saturated artificially cemented and noncemented porous rock samples are given. It is found that the impregnation rate can be increased and gas can be displaced completely from the porous collector on account of the field action.Institute of Oil and Gas Problems, Moscow. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 63, No. 2, pp. 232–236, August, 1992.     

3D elastodynamic crack analysis by a non-hypersingular BIEM

A boundary integral equation method (BIEM) is presented for 3D elastodynamic crack analysis. The method is based on a non-hypersingular BIE formulation, where the unknown quantities are the crack opening dispacements and their derivatives. The numerical scheme applied here uses a constant shape function for elements away from the crack front, and a square-root crack-tip shape function for elements near the crack front to describe the proper behavior of the unknown quantities at the crack front. A collocation method is applied to convert the non-hypersingular BIEs to a system of linear algebraic equations which are solved numerically. For several geometrical configurations, numerical results are presented for both the elastodynamic stress intensity factors and the scattering cross section. They are in good agreement with those obtained by other authors.     

Probing the electromagnetic field distribution within a metallic nanodisk

A Co nanolayer is used as a local probe to evaluate the vertical inhomogeneous distribution of the electromagnetic (EM) field within a resonant metallic nanodisk. Taking advantage of the direct relation between the magneto-optical activity and the electromagnetic field intensity in the Co layer, it is shown that the nonuniform EM distribution within the nanodisk under plasmon resonant conditions has maximum values close to the upper and lower flat faces, and a minimum value in the middle.