Elastic properties static

Magnesium oxychloride cements are widely used for the fabrication of floors. They find application for this purpose because of their attractive appearance, which resembles marble, and also because of their acoustic and elastic properties and their resistance to the accumulation of static charge. They have also been used for plastering walls, both interior and exterior for exterior walls the cement often includes embedded stone aggregate (Sorrell Armstrong, 1976). However, there have been problems with this latter application, since the base cement has been found to be dimensionally unstable and, in certain circumstances, to release corrosive solutions and show poor weather resistance. 

The important elastic properties of a material undergoing deformation under static tension are stiffness, elastic strength and resilience. For a material obeying Hooke s law, the modulus of elasticity, E (= o/e), can be taken to be a measure of its stiffness. The elastic... 

Other flexible framework calculations of methane diffusion in silicalite have been performed by Catlow et al. (64, 66). A more rigorous potential was used to simulate the motion of the zeolite lattice, developed by Vessal et al. (78), whose parameters were derived by fitting to reproduce the static structural and elastic properties of a-quartz. The guest molecule interactions were taken from the work of Kiselev et al. (79), with methane treated as a flexible polyatomic molecule. Concentrations of 1 and 2 methane molecules per 2 unit cells were considered. Simulations were done with a time step of 1 fs and ran for 120 ps. 

Bockstedte M, Kley A, Neugebaur J, Scheffler M (1997) Density-functional theory calculations for poly-atomic systems electronic structure, static and elastic properties and ab initio molecular dynamics, Comput Phys. Commun. 107 187-222... 

Mechanical testing was conducted on samples 25 mm in length, 10 mm in width and 0.1 mm in thickness, Because of the high compliance of the films, it was difficult to mount an extensometer on the samples to measure E. A DMA was therefore used to assess the elastic properties of the composite samples in the tensile mode of loading. A 5 N static tensile load and displacement amplitude of 16 /tm at a frequency of 1 Hz were applied. Nine measurements for each sample were made and the average values are reported here. 

Straightforward measurements of elastic properties of materials can be made via high-pressure static compression experiments, in which X-ray diffraction (XRD) is used to measure the molar volume (V), or equivalently the density (p), of a material as a function of pressure (P). The pressure dependence of volume is expressed by the incompressibility or isothermal bulk modulus (Kt), where Kp = —V(bP/bV)p. 

Amorphous polymers well above Jg behave either as liquids or, if they are cross-linked, as rubbers the properties of rubbers are discussed in the next section. In the region close to Jg the viscoelastic properties dominate even at small strains and relatively short times and these are considered in the next chapter. This means that the static small-strain properties of amorphous polymers can be discussed meaningfully only when the polymers are well below Tg. Semicrystalline polymers are really composite materials. At temperatures well below the Tg of the amorphous regions the material has small-strain elastic properties that depend on the proper-... 

The accuracy of the model in the lifetime prediction was verified even in this case by comparison between model estimations and experimental fatigue lives. The parameters of the calibration fatigue curves together with the elastic properties of the laminates investigated are listed in Table 7.5. In some cases, elastic and static strength properties not available in the original sources were estimated from constituent properties or taken from literature. 

The basic principle of this method is that the velocity of an ultrasonic wave through a material is related to its density and elastic properties. This is one example of a dynamic method for determining elastic constants, such as Young s modulus and shear modulus. Dynamic methods are more accurate than static methods with uncertainties of <0.5% ( 10% would be more typical for static methods). 

When the application was extended to simulation of crystalline silica and silicate, however, we encounter the fact that these interatomic potentials does not necessarily reproduce important structural properties such as bulk moduli, elastic constants or sometimes even dynamical stability of the crystalline symmetry. Thus some efforts have been made to incorporate crystal structures and their elastic properties into the process of empirical determination of the interatomic potentials by means of a static energy minimization technique [5,6, 7, 8, 9],... 

There are many stress-analysis problems involving viscoelastic materials that are of a statically determinate class, i.e., the stresses in the body depend only on the applied forces and moments and not specifically on the elastic properties of the body. Such problems can be solved by invoking the correspondence principle. Then, the time and temperature dependences of the strains and flexures in the body can be obtained through the time temperature-shift properties of the viscoelastic polymer. 

M. Bockstedte, A. Kley, J. Neugebauer, and M. Scheffler, Comput. Phys. Commun., 107,187 (1997). Density-Functional Theory Calculations for Polyatomic Systems Electronic Structure, Static and Elastic Properties and Ab Initio Molecular Dynamics. 

By measuring the static elastic properties of human thoracic and abdominal aortas in vitro, Langewouters et al. [35] proposed the following empirical relationship between the cross-sectional area of the lumen (A) and the pressure in the vessel (p) ... 

The static continuum theory of elasticity for nematic liquid crystals has been developed by Oseen, Ericksen, Frank and others [4]. It was Oseen who introduced the concept of the vector field of the director into the physics of liquid crystals and found that a nematic is completely described by four moduli of elasticity Kn, K22, K33, and K24 [4,5] that will be discussed below. Ericksen was the first who understood the importance of asymmetry of the stress tensor for the hydrostatics of nematic liquid crystals [6] and developed the theoretical basis for the general continuum theory of liquid crystals based on conservation equations for mass, linear and angular momentum. Later the dynamic approach was further developed by Leslie (Chapter 9) and nowadays the continuum theory of liquid crystal is called Ericksen-Leslie theory. As to Frank, he presented a very clear description of the hydrostatic part of the problem and made a great contribution to the theory of defects. In this Chapter we shall discuss elastic properties of nematics based on the most popular version of Frank [7]. 

Under static conditions, the elastic properties of solids have been studied in case study B2 Elasticity of Solids in Chapter 5, in which the capacitive relationship was modeled by two reduced elastances (elasticities), depending on the mode of deformation, by traction or by shear... 

Table I summarizes studied-material properties. Schramm and Kasen, who studied both mechanical properties and static elastic properties of these composites, gave further materials details.

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