Thermo elastic

Pagano, N.J. and Tandon. G.P. (1990). Thermo-elastic model for multidirectional coated fiber composites Traction formulation. Composites Sci. Technol. 38, 247 269. 

Eq. (III-ll) forms the basis for obtaining conformational information from deformation experiments as a function of temperature, commonly referred to as thermo-elasticity ... 

This deficiency is also demonstrated by the more recent experimental findings that the thermo-elasticity equation (Eq. III-12) does not yield a constant value for 3 In(r2 jd T (37, 132, 145, 146, 158, 162, 183). This has sometimes been ascribed to the experimental difficulty in converting (3 ln(flT)ldT )Ll, into the desired quantity (3 ln(//Z )/3T) y. 

In the swollen state the situation is somewhat better. In many swollen networks Eq. (III-26) is reasonably well obeyed and the application of the thermo-elasticity equation yields a 3 In 0/3 T value which is reasonably independent of the deformation at least in good diluents (46). It should be pointed out that the experimental error in measuring the thermoelasticity of open, swollen systems is quite appreciable. This derives from the fact that the conversion term for an open system is more complicated because of the change in diluent content with temperature (86,87) ... 

It should also be remembered that (r2 0 in a swollen network does not with certainty refer to -dimensions, so that the conformational information, obtained from 8 In (r fd T through thermo-elasticity, should be viewed with some caution. 

TWO PHASE FLOW IN CAPILLARY POROUS THERMO-ELASTIC MATERIALS... 

Abstract In this contribution, the coupled flow of liquids and gases in capillary thermoelastic porous materials is investigated by using a continuum mechanical model based on the Theory of Porous Media. The movement of the phases is influenced by the capillarity forces, the relative permeability, the temperature and the given boundary conditions. In the examined porous body, the capillary effect is caused by the intermolecular forces of cohesion and adhesion of the constituents involved. The treatment of the capillary problem, based on thermomechanical investigations, yields the result that the capillarity force is a volume interaction force. Moreover, the friction interaction forces caused by the motion of the constituents are included in the mechanical model. The relative permeability depends on the saturation of the porous body which is considered in the mechanical model. In order to describe the thermo-elastic behaviour, the balance equation of energy for the mixture must be taken into account. The aim of this investigation is to provide with a numerical simulation of the behavior of liquid and gas phases in a thermo-elastic porous body. 

Keywords Theory of Porous Media (TPM), ternary model, capillarity, thermo-elasticity... 

Additionally, the thermo-elastic behaviour will be described. Although, not all constitutive relations can be identified right now, the theoretical treatment of the entropy inequality is finished for the three phase model. 

Two Phase Flow in Capillary Porous Thermo-Elastic Materials... 

For further particulars concerning the thermo-elastic modelling of the solid including the constitutive equations with the heat flux q and the internal energy we refer you to Bluhm [5]. 

Bluhm, J. (2002) Modelling of saturated thermo-elastic porous solids with different phase temperatures, in Porous Media Theory, Experiments and Numerical Applications, W. Ehlers, J. Bluhm (eds.), Springer-Verlag, Berlin/Heidelberg/New York... 

Kerner, E. H., "The Elastic and Thermo-elastic Properties of Composite Media, Proc. Phvs. Soc. London. B, 1956, pp. 808-813. 

Kemer, E. H. 1956. Xhe elastic and thermo-elastic properties of composite media. Proc. Phys. Soc. Sect. B69 808-813. 

It has been proposed that the absorption of ultrasound energy depends on the thermo-elastic relaxation of ice crystals in food and is affected by ice crystal orientation and size, impurities present in the ice crystals, as well as temperature (Kissam et al., 1981). Miles and Shore (1978) and Shore et al. (1986) found that ultrasound was more attenuated in frozen meats than in unfrozen tissues and that the attenuation increased markedly with temperature, reaching the maximum near the initial freezing points of the foods before decreasing rapidly at higher temperatures, thus making ultrasound particularly suitable for the controlled thawing of foods (Miles et al., 1999 Torley and Bhandari, 2007). 

In our contribution, we address this aspect and describe numerical methods based on the use of efficient iterative solvers, which exploit the conjugate gradient (CG) method, its generalization and the space decomposition preconditioners. The efficiency of these solvers will be illustrated by the solution of elasticity and thermo-elasticity problems arising from the finite element analysis of selected benchmarks with computations performed on a PC cluster. The introduced ideas could be useful also for the solution of more complicated coupled problems. 

In this section, we describe problems of thermo-elasticity and focus on their robust numerical solution. The considered problems are important for the investigation of nuclear waste repositories, as is illustrated by the simple model problem shown in Figure 1. 

The thermo-elasticity problem is to find the temperature r and displacement u, ... 

The layout of the CERTI concept being considered in a hard geological medium, a simple thermo-elastic law has been chosen to describe the behavior of the rock. Together with the mechanical equilibrium equation, it leads to a relation between the displacement vector u and the temperature T besides, deformations and stresses tensors can be derived from the classical following equations ... 

The analysis presented here assumes that bulging and thermo-elastic effects in either diamond and ZnSe can be neglected [27, 52-54]. The assumed configuration for each case is that of a circular window, 25 mm in diameter, which is edge... 

The Lagrangian Implicit Model The Lagrangian implicit model was also used to study cutting processes. In this model, the work-piece is represented by a thermo-elastic-plastic material. The FEM codes consider the contact between solid bodies, different friction models, and chip separation criteria. 

Moreover, rubbers exhibit unique thermo-elastic effects unknown in metals, as noted first by Gough as early as 1805. Gough (1805) reported two distinctive responses, namely that (a) a rubber when held stretched under a constant force contracts reversibly on heating, and (b) it gives off heat reversibly when stretched at constant temperature (Treloar 1975). These important characteristics that were confirmed later by Joule (1859) are now referred to as the Gough-Joule effect and are key in the mechanistic understanding of the elastic behavior of rubbers. 

The thermal expansion coefficient and thermal conductivity of the COI 720 material are orthotropic, but with lower anisotropy than the elastic properties, as Table 7 indicates. The thermo-elastic properties are reasonably computed by micromechanical models that incorporate both porosity and microcracking in the matrix [146]. 

The anisotropy of the composite strength is even greater than the anisotropy of the thermo-elastic properties (Table 8). The ultimate strength of specimens loaded in a 45° tensile configuration is approximately 20% of the fiber-direction strength. Failure... 

L Kelvin. On the thermo-elastic and thermal-magnetic properties of matter. Transactions of the Royal Society of Edinburgh, 20(1) 161, 1853. 

The viscous-elastic model, also called the thermo-elastic model, was proposed by Struik (1990). The model assumes that the thermal elastic parameters are constant and independent of temperature below as well as above the soUdihcation temperature T, and that the only discontinuous changes occur at Tj. Usually, the material is assumed to be hquid and to sustain no stresses above T, while below Ts the material is assumed elastic and able to sustain stresses. Under this assumption we have... 

Tiersten HE (1971) On the nonlinear equations of thermo-elasticity. Int J Engng Sci 9 587... 

Monte Carlo simulations have been used to calculate thermo-elastic results through the temperature coefficient of the unperturbed dimensions. In the case of networks of the protein elastin, such results were used to evaluate alternative theories for the molecular deformation mechanism for this bioelastomer. ... 

Kang, S.-H. Im, Y.-T. (1987). Three dimensional thermo-elastic-plastic finite element modeling of quenching process of plain-carbon steel in couple with phase transformation. Int.. Mech. Sci., Vol. 49,423-439. 

Lubarda VA (2004) Constitutive theories based on the multiplicative decomposition of deformation gradient Thermo-elasticity elastoplasticity and biomechanics. Appl Mech Rev 57 95-108 Lubliner J (1990) Plasticity theory. Collier-MacmiUan, New York McQuarrie DA, Simon JD (1997) Physical chemistry. University Science Books, Sausahto Malvern LE (1969) Introduction to the mechanics of a continuous medium. Prentice-HaU, Englewood Cliffs... 

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