Orienting element models

When the polymer was stretched the units of the aggregate would be aligned, without the units themselves being altered. Thus, in principle, the mechanical properties of partially oriented polymers might be derived in terms of the d ree of molecular orientation and the properties of specimens with maximum orientation. We shall consider only uniaxial stretching, i.e. fibre orientation, and the treatment will follow that given by Ward, - and by Hadley et al.  

The calculation of the elastic constants of the partially oriented polymer can be made in two ways. One can assume either uniform strain throughout the aggregate, which involves a summation of stiffness constants, or uniform stress, which implies a summation of compliance constants. In the former case the tractions across the boundaries of the unit do not satisfy the stress equilibrium conditions in the latter case there is discontinuity 

For an isotropic aggregate, the stiffness averaging procedure had been proposed by Voigt, ° and the compliance averaging procedure by Reuss, many years previously. Each had been used to compare the elastic constants of single crystals with those of an isotropic aggregate of single crystals (see for example Ref. 12). 

The equations which predict the elastic constants of a partially oriented polymer involve orientation functions to define the orientation of the aggregate units. For example, the average extensional compliance S33 for a transversely isotropic aggregate of transversely isotropic structural units is given by S 33 = Su sin 0+S33Cos 0-l-(2Si3-l-544) sin 0cos 9. 

MEASURED EXTENSIONAL AND TORSIONAL COMPLIANCES OF UNORIENTED POLYMERS COMPARED WITH REUSS AND VOIGT AVERAGE PREDICTIONS FOR AN AGGREGATE MODEL. 

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Two distinct types of macroscopic theoretical model for the low strain mechanical behaviour of oriented solid polymers will be considered in this chapter. First, models which predict the changes in elastic constants with the development of orientation these will be referred to as orienting element models. Secondly, models which seek to explain the mechanical behaviour of both isotropic and oriented polymers in terms of a two phase material with separate components representing crystalline and amorphous fractions these we shall call composite structure models. 

To understand and optimize the electro-optic properties of polymers by the use of molecular engineering, it is of primary importance to be able to relate their macroscopic properties to the individual molecular properties. Such a task is the subject of intensive research. However, simple descriptions based on the oriented gas model exist [ 20,21 ] and have proven to be in many cases a good approximation for the description of poled electro-optic polymers [22]. The oriented gas model provides a simple way to relate the macroscopic nonlinear optical properties such as the second-order susceptibility tensor elements expressed in the orthogonal laboratory frame X,Y,Z, and the microscopic hyperpolarizability tensor elements that are given in the orthogonal molecular frame x,y,z (see Fig. 9). 

A finite-element mesh was constructed as shown in Figure 5. The hydrological properties of the different units within the finite-element model was first estimated from local geohydrological field data and then calibrated to match observed head distribution and inflow into the open drift. An initial stress was assigned according to = 10 MPa, Oh = 15 MPa, and On = 30 MPa, where Oh is oriented 45° from the axis of the FEBEX tunnel (Figure 5b). These values are within the range of stress measurements in the GTS area (Pahl el al.. 1989). 

This paper presented the thermo-hydraulic (TH) coupled finite element model that we developed within the object-oriented simulator RockFlow. The governing equations, their numerical implementation, and the algebraic equations, as well as available coupling schemes for the RockFlow TH model were presented. 

Finite element modelling of the effects of a 14% volume fraction of glass fibre with an aspect ratio of 30 (Fig. 4.29b), used fibre orientations that fitted a maximum entropy distribution. It predicted that the longitudinal Young s modulus increased non-linearly with cos B, and that constant strain conditions applied for averaging the properties of the unidirectional composite. 

However, especially for three-dimensional stmcture, or, even, in two-dimensional stmcture with significant out-of-plane loads, the stiffness averaging of the classical laminated plate theory is not sufficient. In such cases, a specialized finite element model such as the binary model by Cox, Carter, and Fleck [25] can be used. In this model, Monte Carlo simulation allows the user to randomly orient tows and to randomly assign strength properties to the different components. 

Another two-dimensional, discrete element model was applied by Cartaxo and Rocha [43]. In this work, only the dynamic phenomena were investigated, that is, heat and mass transfer between the phases were not considered. Thns, the inflnence of the momentum coupling between the discrete particles and the conveying air on the air radial velocity and the mass concentration profiles was presented. An object-oriented numerical model was developed to simulate the conveying of large spherical particles (3 mm) through 9.14 m vertical tube with 7.62 cm bore size. 

More recently this model has been modified so that it resembles a system of oriented elements, which are subjected to elongation as well as rotation from their initial position. The orientation distribution function is obtained by optimising the total energy of the system. 

Then the equilibrium response acting on the network orientation element can be defined following the Arruda-Boyce eight-chain model [40] as... 

Safety and risk management research in healthcare has adopted as its dominant trend the systems oriented approach, modelled largely on previous research in safely critical industries such as aviation and nuclear power. The systems view entails that the focus is not primarily on the mechanisms of individual human error but on the factors that shape human performance (Rasmussen 1986 Reason 1993,1997). In an organisational context, such factors are, of course, those that are within the control of the organisation. For instance, it has been suggested that quahty and safety are affected not only by operators professional and technical competence and skills, but also by their attitudes to and perceptions of their job roles, their organisation and management (Helmreich and Merritt 1998). Such employee attitudes and views are important elements which shape safety cirlture - and its related notion safety climate . Indeed, survey studies have shown that staff attitudes are important indices of safety performance not only in human-machine system domains such as railway operations and constmction (e.g. Itoh and Andersen 1999 Itoh et al. 2004 Silva et al. 2004) but also in healthcare (e.g. Colla et al. 2005 Itoh and Andersen 2010). 

Instantaneous fiber shortening ranging from 4% to 14% were obtained. In arriving at these fiber contraction data, the fibers were assumed to be circumferentially oriented. This leads to the discussion of another advantage of using the finite element models, in that the fibrous properties of the myocardium and its changes of orientation across the ventricular wall thickness can be easily incorporated. 

Guideline 5 establishes the criteria for local locations in terms of the SCL and SCP, and the orientation for the SCL-SCP caused by a discontinuity or blend radius. The blend radii are normally included in the finite-element model. 

Dong Y, Bhattacharyya D, Hunter PJ. Experimental characterisation and object-oriented finite element modeling of polypropylene/or-ganoclay nanocomposites. Compos Sci Tech-nol 2008 68 2864-75. 

Doug Y, Bhattacharyya D and Hunter P J (2007) Characterisation and Object-Oriented Finite Element Modelling of Polypropyleue/Organoclay Nanocomposites, Key Eng Mater 334-335 841-844. 

The theory of spherical diqtersion has been applied successfully to some oriented polymers, and the piezoelectric constants for the crystalline phase have been estimated. However, there still remain problems such as the interface between the crystalline phase and the amorphous phase. Actually, for oriented films of poly- y-benzylglutamale. the simple spherical dispersion model is not applied satisfactorily, and the extended three-element model, taking account of grain boundaries, has lo be introduced to explain the etywrimental results. Further elaboration of this model would be useful to understand the texture and properties of a composite such as a mixture of piezoelectric ceramic particles and polymers. 

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