Orthotropic particles

A body has a plane of symmetry if the shape is unchanged by reflection in the plane. Orthotropic particles have three mutually perpendicular planes of symmetry. An axisymmetric particle is symmetric with respect to all planes containing its axis, so that it is orthotropic if it has a plane of symmetry normal to the axis, i.e., if it has fore-and-aft symmetry. 

For an orthotropic particle in steady translation through an unbounded viscous fluid, the total drag is given by Eq. (4-5). In principle, it is possible to follow a development similar to that given in Section IT.B.l for axisymmetric particles, to deduce the general behavior of orthotropic bodies in free fall. This is of limited interest, since no analytic results are available for the principal resistances of orthotropic particles which are not bodies of revolution. General conclusions from the analysis were given in TLA. 

The only orthotropic particles for which comprehensive experimental results are available are square bars, rectangular parallelepipeds with one pair of square faces. Symmetry then shows that the two principal resistances corresponding to translation with square faces parallel to the direction of motion are equal. These resistances will be denoted by c 2, while the resistance for translation normal to the square faces will be called cy. Consider such a particle in arbitrary translation at velocity U. Figure 4.11 shows a section of the particle parallel to the square faces (72 is the component of U in this plane, and the angle between U2 and principal axis 2 is 0. From Eq. (4-5), the drag components are as shown in Fig. 4.11. Hence the drag component parallel to U2 is... 

The book by Clift et al. (1978) contains an extensive review on this subject. The treatment is, however, mostly for the axisymmetric particles such as spheroids and cylinders and orthotropic particles such as rectangular parallelepipeds. For particles of arbitrary shape. 

J. S. Cintra and C. L. Tucker, Orthotropic closuere approximations for flow-induced fiber orientation, J. Rheol. 39, 1095-1122 (1995) C. V. Chaubal, A. Srinivasan, O. Egecioglu, and L. G. Leal, Smoothed particle hydrodynamics technique for the solution of kinetic theory problems. Part 1. Method, J. Non-Newtonian Fluid Mech. 70, 125-54 (1997). 

Physical properties of blends consisting of a continnons matrix and one or more dispersed (discrete) components can be predicted by nsing adapted models proposed for particulate composite systems (216-220). Most of these models do not consider effects of the particle size, but only of volnme fractions of components in the system. Thus, the increase in particle size dne to particle coalescence is not presumed to perceptibly affect mechanical properties, except for fractnre resistance, which is controlled by particle size and properties of dispersed rnbbers. As polymer blends with three-dimensional continuity of two or more components are isotropic materials, simple parallel or series models or models for orthotropic or quasi-isotropic materials are not applicable. Physical properties of blends with partially co-continuous constituents can be calculated by means of a predictive... 

Dias et al. [71] presented a computational model for plain woven fabrics which can represent known elastic behavior in deformation such as planar extension, shearing and out-of-plane bending, drape, and buckling. They assumed the fabric to be an orthotropic linear elastic continuum and discretized by a mesh of triangles. Then each triangle links three particles which are capable to measure the stress and strain of the imderlying medium. For the planar deformation, they assume the hypothesis of the plate imder plane stress Irom the classical theory of elasticity. For the out-of-plane deformation, they allow linear elasticity and... 

Compressive gaskets for high temperature applications are usually made of either vermiculite, phlogopite mica or muscovite mica. Exfoliation results in highly compliant structures made of crystal platelets or fine particles. The CTE of such materials is likely very complex and its measurement challenging. Depending on the manufacturing process, an orthotropic behaviour is expected. The scarce available data indicates that it lies within 10—14 x 10 between RT and 1073 K [34]. 

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