Thermal instability of a layered rectangular viscoelastic prism under high-frequency compressive loading

The thermal instability of a rectangular prism under vibrational heating is studied solving a coupled problem of thermoviscoelasticity and using finite-element modeling. The prism has copper and polyethylene or polymethylmethacrylate layers and undergoes high-frequency mechanical or kinematic compression. It is established that in the case of polyethylene, thermal instability occurs under mechanical loading and does not occur under kinematic loading. In the case of polymethylmethacrylate, thermal instability occurs under both kinds of loading. This is because of the increase in the shear and bulk loss compliances with temperature for each of the polymers. At the transformation temperature, shear dissipation goes over into bulk dissipation, which is predominant in rather thin polymeric layers. Dynamicity influences the critical loads both qualitatively and quantitatively     

Vibrations and self-heating of a viscoelastic prism with a cylindrical inclusion

The vibrations and self-heating of a viscoelastic prism with a cylindrical inclusion under harmonic loading are studied through numerical simulation. The effects of the stiffness of the inclusion and the mechanical and kinematic types of loading on kinetics, spatial temperature distribution, and thermal instability parameters are examined __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 6, pp. 73–81, June 2007.     

Change in the stress intensity factors for plane cracks in a transversely isotropic medium due to thermal loads

The feasibility of controlling the stress intensity factors for plane cracks of arbitrary form (distributed in a plane perpendicular to isotropy axis in a transversely isotropic material) which are subjected to symmetric mechanical loading by heating the material is demonstrated by using the congruence theorem and making an analogy between isotropic and transversely isotropic materials based on the theory of thermoelasticity. It is shown that a thermal load which fully compensates for the mechanical load can be created within the range in which the material behaves linearly. If it turns out to be technically impossible to create the necessary thermal load, a simpler temperature regime can be chosen that will “cancel” the mechanical force field with a certain factor of safety. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 9, pp. 29–37, September, 1999.     

Analysis of the ultimate kinematic characteristics of railgun accelerators of solids

A comparative analysis of the dependences of the ultimate (under heating conditions) velocity on the dimensions and thermal properties of the projectile and on the length of the railgun is performed on the basis of a numerical solution of two-dimensional unsteady equations of magnetic-field diffusion and heat transfer. Homogeneous and multilayer projectiles and homogeneous rails and rails with a resistive coating are considered. It is shown that the ultimate kinematic characteristics of railgun accelerators of solids can be considerably increased by changing the structure and thermal properties of the materials of the projectile and the electrodes. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 156–162, March–April, 1999.     

Forced vibrations and vibroheating of shallow viscoelastic laminated shells with the piezoelectric effect

The vibrations and dissipative heating of a hinged shallow shell made of viscoelastic piezoelectric material and subject to harmonic electric loading are considered. The basic relations are obtained by using the Kirchhoff-Love mechanical hypotheses supplemented with the respective hypotheses for electric quantities. Analytical solutions of both electromechanical and thermal problems are derived for the case where the temperature is constant along the shell thickness. Translated from Prikladnaya Mekhanika, Vol. 36, No. 6, pp. 78–87, June, 2000.     

Generalized thermoelastic analysis of the stress-focusing effect in a solid cylinder under rotationally asymmetrical instantaneous thermal loading

Summary  This paper investigates the stress-focusing effect in an infinitely long cylinder under rotationally asymmetrical instantaneous thermal loading on the basis of the generalized thermoelastic Lord–Shulman (L-S) and Green–Lindsay (G-L) theories. Combined forms of the governing equations of both theories are given in a cylindrical coordinate system. The two-dimensional generalized thermoelastic problems are solved by numerical inversion of Laplace transform. Calculations have been performed to find distributions of thermal stresses on the basis of the L-S theory. Stress-focusing phenomena under different heating conditions are presented. The effects of thermomechanical coupling and relaxation time on the stress-focusing phenomena as well as the singularity of stresses are discussed. Received 15 November 2000; accepted for publication 15 November 2001     

Basic equations of the theory of thermoviscoelastic plates with distributed sensors and actuators

The basic equations of the theory of thermoviscoelastic thin-walled plates with piezoelectric sensors and actuators under monoharmonic mechanical and electric loading are derived using the Kirchhoff–Love hypotheses. The thermomechanical behavior of passive and piezoactive materials is described using the concept of complex characteristics. Methods of solving nonlinear problems of active damping of thermomechanical vibrations of plates with sensors and actuators are considered. The effect of dissipative heating on the damping of axisymmetric vibrations of a thermoviscoelastic solid circular plate is analyzed as an example     

Single-frequency vibrations and vibrational heating of a piezoelectric circular sandwich plate under monoharmonic electromechanical loading

The forced monoharmonic bending vibrations and dissipative heating of a piezoelectric circular sandwich plate under monoharmonic mechanical and electrical loading are studied. The core layer is passive and viscoelastic. The face layers (actuators) are piezoelectric and oppositely polarized over the thickness. The plate is subjected to harmonic pressure and electrical potential. The viscoelastic behavior of the materials is described by complex moduli dependent on the temperature of heating. The coupled nonlinear problem is solved numerically. A numerical analysis demonstrates that the natural frequency, amplitude of vibrations, mechanical stresses, and temperature of dissipative heating can be controlled by changing the area and thickness of the actuator. It is shown that the temperature dependence of the complex moduli do not affect the electric potential applied to the actuator to compensate for the mechanical stress __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 1, pp. 79–89, January 2008.     

Fundamental-solution methods in stress-concentration problems for thin elastic shells

This paper deals with fundamental-solution methods applied to stress-concentration problems for thin elastic shells. Publications concerned with the relevant division of the theory of plates and shells are reviewed. The theories behind the methods are described, and specific results for static and dynamic concentrated loads are presented. The capabilities of the methods are illustrated by fracture problems for orthotropic shells with notches and holes under mechanical loading and for isotropic shells with notches under thermal loading __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 3–25, July 2007.     

Dynamics of a chain system of rigid bodies with gravity-friction seismic dampers: fixed supports

A design model for a chain system of N elastically linked rigid bodies with a spheroidal gravity-friction damper is proposed. The Lagrange–Painlevé equations of the first kind are used to construct nonlinear dynamical models of a mechanical system undergoing translational vibrations about the equilibrium position. The conditions under which the system moves in one plane are established. The double nonstationary phase–frequency resonance of a system with N = 2 is analyze. After the numerical integration of the systems of differential equations, the phase–frequency surfaces are plotted and examined for several combinations of system parameters under two-frequency loading     

Theoretical model of acoustic emission under mechanical loading of rocks in the maximum compaction region

A theoretical model of changes in acoustic emission activity in a geomaterial under continuous or stepwise mechanical loading is justified. Based on this model, the experimentally found laws of emission in the region of the maximum compaction of rock samples with different rates of mechanical loading of these samples are analyzed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 145–152, July–August, 2006.     

Axisymmetric thermoelastoplastic stress-strain state of transversely isotropic laminated shells

The method of successive approximations is used to determine the thermoelastoplastic stress-strain state of isotropic and transversally isotropic laminated shells of revolution under axisymmetric loading. Hill’s theory of plasticity with isotropic hardening is used to describe the deformation of transversely isotropic materials, while the theory of deformation along paths of small curvature is used to describe the deformation of isotropic materials. The elastoplastic stress-strain state of a two-layer cylindrical shell under mechanical and thermal loads is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 6, pp. 71–80, June 2006.     

State-space approach of two-temperature generalized thermoelasticity of infinite body with a spherical cavity subjected to different types of thermal loading

In this work, we will consider an infinite elastic body with a spherical cavity and constant elastic parameters. The governing equations are taken in the context of the two-temperature generalized thermoelasticity theory (Youssef in J Appl Math Mech 26(4):470–475 2005a, IMA J Appl Math, pp 1–8, 2005). The medium is assumed initially quiescent. Laplace transform and state space techniques are used to obtain the general solution for any set of boundary conditions. The general solution obtained is applied to a specific problem when the bounding plane of the cavity is subjected to thermal loading (thermal shock and ramp-type heating). The inverse Laplace transforms are computed numerically using a method based on Fourier expansion techniques. Some comparisons have been shown in figures to estimate the effect of the two-temperature and the ramping parameters.     

Kinematics of finite-strain elastic-inelastic deformation

Polar decomposition tensors are constructed for slightly disturbed kinematic elastic, inelastic, and thermal strain tensors. Provided that the inelastic and thermal site gradients are pure deformations without rotations, relations are obtained between inelastic small strains and small rotations and between thermal small strains and small rotations which transform an intermediate configuration to a close current configuration. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 165–172, January–February, 2008.     

Erratum to: Experimental Investigation on Mechanical Behavior of Coarse Marble Under Six Different Loading Paths

A series of triaxial compression experiments were preformed for the coarse marble samples under different loading paths by the rock mechanics servo-controlled testing system. Based on the experimental results of complete stress-strain curves, the influence of loading path on the strength and deformation failure behavior of coarse marble is made a detailed analysis. Three loading paths (Paths I–III) are put forward to confirm the strength parameters (cohesion and internal friction angle) of coarse marble in accordance with linear Mohr-Coulomb criterion. Compared among the strength parameters, two loading paths (i.e. Path II by stepping up the confining pressure and Path III by reducing the confining pressure after peak strength) are suggested to confirm the triaxial strengths of rock under different confining pressures by only one sample, which is very applicable for a kind of rock that has obvious plastic and ductile deformation behavior (e.g. marble, chalk, mudstone, etc.). In order to investigate re-fracture mechanical behavior of rock material, three loading paths (Paths IV–VI) are also put forward for flawed coarse marble. The peak strength and deformation failure mode of flawed coarse marble are found depending on the loading paths (Paths IV–VI). Under lower confining pressures, the peak strength and Young’s modulus of damage sample (compressed until post-peak stress under higher confining pressure) are all lower compared with that of flawed sample; moreover mechanical parameter of damage sample is lower for the larger compressed post-peak plastic deformation of coarse marble. However under higher confining pressures (e.g. σ ₃ = 30 MPa), the axial supporting capacity and elastic modulus of damage coarse marble (compressed until post-peak stress under lower confining pressure) is not related to the loading path, while the deformation modulus and peak strain of damage sample depend on the difference of initial confining pressure and post-peak plastic deformation. The friction among crystal grains determines the strength behavior of flawed coarse marble under various loading paths. In the end, the effect of loading path on failure mode of intact and flawed coarse marble is also investigated. The present research provides increased understanding of the fundamental nature of rock failure under different loading paths.     

Extending the Bodner–Partom model to simulate the response of materials with extreme kinematic hardening

This paper demonstrates that, at extreme levels of kinematic hardening, the traditional formulation of the Bodner–Partom model can produce anomalous results. The reasons for this anomalous behaviour are explained, and a reformulated version of the model is presented. This reformulation extends the range of the model to include levels of kinematic hardening that may be problematic in the traditional formulation. The formulation of the model is adjusted so as to retain the rate dependency of the original Bodner–Partom model; and to permit the values of the material parameters used with the traditional formulation to be re-used with the extended model—with the exception only of the hardening coefficients which become dimensionless constants holding different numerical values. This revised formulation also imposes associated flow, thereby ensuring phase consistency between stress and plastic strain during non-proportional loading. In this way, the anomalies are removed, the range and stability of the model is increased, and all the advantages and important features of the Bodner–Partom model are retained.     

One model of fatigue crack growth

A model for crack growth is proposed based on studies of the variation in the curvature radius at the crack tip during cyclic loading. Relations are obtained between mechanical material characteristics, crack geometry, and the rate of crack growth in a structure under cyclic loading. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 167–175, July–August, 2009.     

On finite-element solution of spatial thermoviscoelastoplastic problems

A finite-element algorithm is proposed for the analysis of the thermoviscoelastoplastic stress-strain state of bodies under complex loading (thermal and mechanical). It is assumed that an arbitrary element of the body deforms along a rectilinear or slightly curved path. The three-dimensional stress-strain state of the body’s elements is determined using the iterative method of additional strains. The technique is tested by analyzing the three-dimensional viscoelastic stress-strain state of a hollow cylinder and the thermoplastic state of a disk __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 16–25, May 2006.     

Failure of a circular reinforced concrete plate against dynamic fluctuating loads

Summary The kinematic shakedown method is used to evaluate the dynamic cyclic collapse loads for a clamped reinforced concrete plate. The method, based on reduced kinematic formulae recently derived by the author, requires determination of the fictitious elastic fields within the plates, in particular – their envelope corresponding to the external loads, and construction of potential incremental collapse mechanisms. The load amplitude-frequency diagrams constructed should help to choose the necessary reinforcements for the plate under given loading conditions. Received 14 January 1998; accepted for publication 25 June 1998     

Effect of local heat supply to a turbulent boundary layer on the friction

The results of calculating a supersonic turbulent boundary layer on a flat plate in the presence of thermal energy supply to the boundary layer are presented. Two methods of energy supply are considered: heating a local interval of the surface, which is otherwise thermally insulated and using a local volume heat source. It is shown that for the same amount of heat supplied to the gas volume heating leads, under certain conditions, to greater friction reduction than the surface heating. Localization of the energy supply zone leads to the intensification of the viscous drag reduction effect and to a greater decrease in the local friction coefficient, which extends a considerable distance downstream. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 48–56, January–February, 1997. The work was carried out with financial support from the Russian Foundation for Fundamental Research (project No. 93-013-17600).