The relaxation effects of the volume properties of electrically conducting viscoelastic material

A new model of the equations of generalized thermo-viscoelasticity for an electrically conducting isotropic media permeated by a primary uniform magnetic field, taking into consideration the rheological properties of the volume, is given. The formulation is applied to both generalizations, Lord–Shulman theory and the Green–Lindsay theory, as well as to the coupled theory.

The state space approach is adopted for the solution of one-dimensional problems in the absence or presence of heat sources. The Laplace-transform technique is used. A numerical method is employed for the inversion of the Laplace transforms. Numerical results for the stress distribution are given and illustrated graphically for each problem.

Comparisons are made with the results predicted by the three theories, or ignoring the viscous effects of the volume. Also, the effect of the magnetic field is studied. It is found that the consideration of these effects is to decrease the thermal stresses.     

Effects of modified Ohm’s and Fourier’s laws on generalized magneto-viscoelastic thermoelasticity with relaxation volume properties

A model of the equations of the linear theory of generalized thermo-viscoelasticity for an electrically conducting isotropic media permeated by a primary uniform magnetic field, taking into account the rheological properties of the volume, is established. The modified Ohm’s law, including the temperature gradient and charge density effects, and the generalized Fourier’s law, including the current density effect, to the equations are considered. A normal mode analysis is applied to obtain the exact formulas of temperature, displacement, stresses, electric field, magnetic field and current density. Application is employed to our problem to get the solution in the complete form. The considered variables are presented graphically and discussions are made.     

Determination of the relaxation modulus of a linearly viscoelastic material

In this paper, a numerical method for computing the relaxation modulus of a linearly viscoelastic material is presented. The method is valid for relaxation tests where a constant strain rate is followed by a constant strain. The method is similar to the procedure suggested by Zapas and Phillips. Unlike Zapas-Phillips approach, this new method can be also applied for times shorter than t ₁/2, where t ₁ denotes time when the maximum strain is achieved. Therefore this method is very suitable for materials that experiences fast relaxation. The method is verified with numerical simulations. Results from the simulations are compared with analytical solution and Zapas-Phillips method. Results indicate that the presented approach is suitable for estimating the relaxation modulus.     

1D applications on fractional generalized thermoelasticity associated with two relaxation times

Here, this work is concerned with some different one-dimensional (1D) problems of distribution of the thermal stresses and temperature in fractional generalized thermoelastic material, as follows: (i) 1D problem for a half-space of elastic material in the presence of heat sources has been solved by using Laplace transform and state space techniques; and (ii) 1D problem of distribution of thermal stresses and temperature in infinite medium with a spherical cavity subjected to a sudden change in the temperature of its internal boundary, which is assumed to be traction free, has been solved by Laplace transform and direct approach techniques. In the preceding problems, the numerical results for dimensionless variable fields are given and illustrated graphically. According to the numerical results, some comparisons have been shown in figures to estimate the effect of the fractional derivative parameter α about the new theory on all variable fields and discussion has been established for a copper-like material.     

Plane waves in generalized thermoelasticity

The properties of two dilatational motions in the context of generalized thermoelasticity are studied. The exact solution to the frequency equation is given and the exact values of the real and imaginary parts of the wave number are calculated. Approximate representations of this solution are derived for large and small frequencies, along with the ranges of validity. In this context the wave motions are unchanged for small frequencies, but both are modified at large frequencies. The major modifications concern only the thermal wave: the phase velocity approaches a constant value as frequency increases without limit; and the specific loss does not have any local extremum. Finally, the behaviour of amplitude ratios for small and large frequencies is discussed and the results obtained here are compared with those of earlier investigations in coupled thermoelasticity.     

Growth and decay in generalized thermoelasticity

A theory of linear thermoelasticity has been proposed by Green and Lindsay [J. Elasticity 2 (1972) 1-7]. Using their theory we treat the thermoelastic problem for a semi-infinite cylinder where the lateral surface of the cylinder is held either at zero temperature and zero displacement, or at zero heat flux and zero traction. Growth and decay bounds for the energy are derived.     

Variational theorem of generalized Cosserat-medium thermoelasticity

An equation which represents the content of the variational theorem of generalized Cosserat-medium elasticity is introduced. It is shown that, on the basis of this theorem, the basic energy equation of this medium may be obtained.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 1, pp. 139–142, January, 1981.     

The spherical problem for a linear viscoelastic material with environment-dependent properties

This paper is concerned with linear viscoelastic materials whose mechanical properites are affected by environmental factors such as temperature, and by ageing. Solutions are given for mixed and unmixed boundary value problems in a thickwall spherical shell. The environment fields are radially symmetric, but arbitrarily time-dependent. The solutions may be calculated to any required degree of accuracy by considering a sufficient number of terms in the solution series.     

On conservation laws in generalized dynamic thermoelasticity

The differential equations of generalized dynamic thermoelasticity constitute a coupled non-self-adjoint system of PDEs, which in its variational form does not admit a Lagrangian. However following exterior calculus methodology, we augment the space of dependent variables, accompanying the initial differential equations with suitable adjoint equations and additional auxiliary “fields”. So the construction of a Lagrangian is now possible along with the realization of Noether's theory for finding conservation laws. Finally, in our case, it is possible to characterize the additional dependent variables in terms of the physical fields themselves and obtain then conservation laws expressed via the original known thermoelastic fields.     

Equations of generalized thermoelasticity of cosserat medium

Dynamic equations of generalized thermoelasticity are derived for the Cosserat continuum, the theorem of uniqueness of solution of the problem is proved, and an expression is derived which represents the content of a theorem analogous to the reciprocal theorem.Notation absolute temperature - d surface element - Euler radius vector of a point - r Lagrange radius vector of a point - n vector of the external normal to the surface - E unit tensor - s entropy per unit volume - q vector of heat flux - w density of volumetric heat release - =(–_o) _o ¹ relative deviation of temperature from the initial value - _o initial absolute temperature of the medium - asymmetric strain tensor - tensor of flexure and torsion - _o constant characterizing the rate of heat propagation - k coefficient of thermal conductivity - A mechanical power of external surface forces - L mechanical power of external body forces - W kinetic energy of strain - potential energy of strain - X dissipation function - temperature potential - U thermal analog of the power of internal sources - Q thermal analog of the power of the surface of sources Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, Wo. 4, pp. 716–723, October, 1980.     

The relaxation effects of a saturated porous media using the generalized thermoviscoelasticity theory

In this paper, a model of the generalized thermoviscoelasticity for a saturated porous media is used. Taking the rheological properties of the volume into consideration, it is developed on the basis of the thermo-hydro-elastodynamic model proposed by the authors. The formulation is applied to the generalized porous thermoviscoelasticity theories: coupling theory, Lord-Shulman theory and Green-Lindsay theory. The general characteristic equations for arbitrary coordinate system are derived using a semi-analytical approach in the Laplace domain. Exact solutions of the saturated porous thermoviscoelastic media, with a cylindrical cavity that is subjected to a time dependent thermal load, are obtained in the absence of heat sources. Numerical results are illustrated graphically employing numerical method for inverting the Laplace transform. Comparisons are made with the results predicted by these theories and the classical theory. In addition, the influence of rheological parameters on the thermoviscoelastic property is analyzed.     

Incremental viscoelastic formulation using generalized variables for thin structures: relaxation differential approach

This paper presents a new incremental formulation in the time domain for linear, non-ageing viscoelastic materials undergoing mechanical deformation. The transformation of the viscoelastic continuum problem from the integral to the differential form is achieved. The formulation is derived from linear differential equations based on a discrete spectrum representation for the relaxation tensor using generalized variables and applied to thin structures. This leads to incremental constitutive formulations using the finite difference integration. Thus, the difficulty of retaining the strain history in computer solutions is avoided. A complete general formulation of linear viscoelastic strain analysis is developed in terms of increments of generalized stresses and strains. An illustrative example is included to demonstrate the method.     

On the plane strain in a generalized theory of thermoelasticity

This paper is concerned with the plane strain in the linear theory of generalized thermoelasticity, proposed by Green and Lindsay[1]. Using the associated matrices method[2], a representation of Galerkin type, is given. This representation is used to derive the solution of the vibration problem corresponding to concentrated body forces and concentrated heat source in an infinite medium.     

On the propagation of waves in layered anisotropic media in generalized thermoelasticity

In view of the increased usage of anisotropic materials in the development of advanced engineering materials such as fibers and composite and other multilayered, propagation of thermoelastic waves in arbitrary anisotropic layered plate is investigated in the context of the generalized theory of thermoelasticity. Beginning with a formal analysis of waves in a heat-conducting N-layered plate of an arbitrary anisotropic media, the dispersion relations of thermoelastic waves are obtained by invoking continuity at the interface and boundary conditions on the surfaces of layered plate. The calculation is then carried forward for more specialized case of a monoclinic layered plate. The obtained solutions which can be used for material systems of higher symmetry (orthotropic, transversely isotropic, cubic, and isotropic) are contained implicitly in our analysis. The case of normal incidence is also considered separately. Some special cases have also been deduced and discussed. We also demonstrate that the particle motions for SH modes decouple from rest of the motion, and are not influenced by thermal variations if the propagation occurs along an in-plane axis of symmetry. The results of the strain energy distribution in generalized thermoelasticity are useful in determining the arrangements of the layer in thermal environment.     

On a mixed problem for the temperature equation in generalized thermoelasticity

Summary In the context of the generalized thermoelasticity theory, a mixed problem for the temperature equation is constructed by starting with a mixed problem for the coupled governing equations for the displacement and temperature fields. The uniqueness of solution of the former problem is established. A method of deducing a solution of the latter problem from that of the former problem is presented.     

Measurement of viscoelastic properties of tissue-mimicking material using longitudinal wave excitation

This paper presents an experimental framework for the measurement of the viscoelastic properties of tissuemimicking material. The novelty of the presented framework is in the use of longitudinal wave excitation and the study of the longitudinal wave patterns in finite media for the measurement of the viscoelastic properties. Ultrasound is used to track the longitudinal motions inside a test block. The viscoelastic parameters of the block are then estimated by 2 methods: a wavelength measurement method and a model fitting method. Connections are also made with shear elastography. The viscoelastic parameters are estimated for several homogeneous phantom blocks. The results from the new methods are compared with the conventional rheometry results.     

Equations of generalized thermoelasticity of a Cosserat medium in stresses

Thermoelasticity equations in stresses are derived in this paper for a Cosserat medium taking into account the finiteness of the heat propagation velocity. A theorem is proved on the uniqueness of the solution for one of the obtained systems of such equations.Notation u displacement vector - small rotation vector - absolute temperature - ₀ initial temperature of the medium - relative deviation of the temperature from the initial value - , , , , , ,, m constants characterizing the mechanical or thermophysical properties of the medium - density - I dynamic characteristic of the medium reaction during rotation - k heat conduction coefficient - ₀ a constant characterizing the velocity of heat propagation - X external volume force vector - Y external volume moment vector - w density of the heat liberation sources distributed in the medium - E unit tensor - T force stress tensor - M moment stress tensor - nonsymmetric strain tensor - bending-torsion tensor - s entropy referred to unit volume - V volume occupied by the body - surface bounding the body - (T)_ki, (M)_ki components of the tensorsT andM - q thermal flux vector Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 482–488, March, 1981.     

The viscoelastic properties of cork

The viscoelastic properties of cork (from Quercus suber) have been investigated in the temperature range –40 to 120°C using the technique of Dynamic Mechanical Analysis (DMA). The results were compared with dielectric data previously reported. A relaxation was detected with a maximum in tan at ca 20°C (f = 1 Hz) and with a mean activation energy of 140 kJ · mol^–1. A decrease in the intensity of the relaxation and an increase of the storage modulus is observed when cork is previously subjected to an annealing process above 60°C. This result is in agreement with previously reported dielectric data. Thermogravimetric experiments seem to confirm that such effect could be caused by the desorption of water molecules. Specimens oriented along the prismatic direction presented higher storage modulus than the ones oriented along the transverse prismatic direction. The rheological properties of cork also showed a dependence upon the mechanical mode used during measurements: for example, the stiffness is the highest for the tensile mode and the lowest for the compression mode.