Lamina, defined

The magnitude of the elastic moduli obtained for an anisotropic material will depend on the orientation of the coordinates used to describe the material elastic response. However, if the material elastic moduli are known for coordinates aligned with the principal material directions, then the elastic moduli for any other orientation can be determined through appropriate transformation equations. Thus, only four elastic constants are needed in order to fully characterize the in-plane maaoscopic elastic response of an orthotropic lamina. The reference coordinates in the plane of the lamina are aligned with longitudinal axis (L) parallel to the fibers, and the transverse axis (7) perpendicnlar to the fibers. The engineering orthotropic elastic moduli of the lamina defined earher are... 

In Section 8.3, the lamina macrostructural elastic moduli have been defined for the principal material directions. The elastic properties are determined experimentally from uniaxial stress states. If these experiments are carried through to failure of the test specimen, then one also obtains the following macromechanical failure strength properties of the lamina defined in principal material coordinates ... 

The basic terminology of fiber-reinforced composite laminates will be introduced in the following paragraphs. For a lamina, the configurations and functions of the constituent materials, fibers and matrix, will be described. The characteristics of the fibers and matrix are then discussed. Finally, a laminate is defined to round out this introduction to the characteristics of fiber-reinforced composite laminates. 

For a unidirectionally reinforced lamina in the 1-2 plane as shown in Figure 2-7 or a woven lamina as in Figure 2-1, a plane stress state is defined by setting... 

Other anisotropic elasticity relations are used to define Chentsov coefficients that are to shearing stresses and shearing strains what Poisson s ratios are to normal stresses and normal strains. However, the Chentsov coefficients do not affect the in-plane behavior of laminaeS under plane stress because the coefficients are related to S45, S46, Equation (2.18). The Chentsov coefficients are defined as... 

Now that the basic stiffnesses and strengths have been defined for the principal material coordinates, we can proceed to determine how an orthotropic lamina behaves under biaxial stress states in Section 2.9. There, we must combine the information in principal material coordinates in order to define the stiffness and strength of a lamina at arbitrary orientations under arbitrary biaxial stress states. 

In Section 2.2, the stress-strain relations (generalized Hooke s law) for anisotropic and orthotropic as well as isotropic materials are discussed. These relations have two commonly accepted manners of expression compliances and stiffnesses as coefficients (elastic constants) of the stress-strain relations. The most attractive form of the stress-strain relations for orthotropic materials involves the engineering constants described in Section 2.3. The engineering constants are particularly helpful in describing composite material behavior because they are defined by the use of very obvious and simple physical measurements. Restrictions in the form of bounds are derived for the elastic constants in Section 2.4. These restrictions are useful in understanding the unusual behavior of composite materials relative to conventional isotropic materials. Attention is focused in Section 2.5 on stress-strain relations for an orthotropic material under plane stress conditions, the most common use of a composite lamina. These stress-strain relations are transformed in Section 2.6 to coordinate systems that are not aligned with the principal material... 

The reduced stiffnesses, Qy, are defined in terms of the engineering constants in Equation (2.66). In any other coordinate system in the plane of the lamina, the stresses are... 

A cross-ply laminate in this section has N unidirectionally reinforced thotropic) layers of the same material with principal material directions srnatingly oriented at 0° and 90° to the laminate coordinate axes. The sr direction of odd-numbered layers is the x-direction of the laminate, e fiber direction of even-numbered layers is then the y-direction of the linate. Consider the special case of odd-numbered layers with equal kness and even-numbered layers also with equal thickness, but not essarily the same thickness as that of the odd-numbered layers, te that we have imposed very special requirements on how the fiber sntations change from layer to layer and on the thicknesses of the ers to define a special subclass of cross-ply laminates. Thus, these linates are termed special cross-ply laminates and will be explored his subsection. More general cross-ply laminates have no such con-ons on fiber orientation and laminae thicknesses. For example, a neral) cross-ply laminate could be described with the specification t/90° 2t/90° 2t/0° t] wherein the fiber orientations do not alter-e and the thicknesses of the odd- or even-numbered layers are not same however, this laminate is clearly a symmetric cross-ply lami-e. 

If the laminae orientation is a random function of z as in Figure 7-53c, define V as the spatial average of the individual Vj(/ B,o) will be treated alike) ... 

The adherence mechanisms involved in Salmonella infection have been studied in great deal. Disease associated with S. enterica serovars is initiated by attachment to and invasion of hosf cells, followed by subse-quenf inflammation of the lamina propria and lymph nodes (Darwin and Miller, 1999). Several genetically defined fimbrial or piliar adhesins con-tribufe fo fhe initial attachment and the overall infection process of Salmonella. Some of fhese include t)q)e 1 fimbriae (Fim), plasmid-encoded (PE) fimbriae, long polar (LP) fimbriae, and thin aggregative fimbriae (curli). However, many ofher putative fimbrial operons have been identified within various S. enterica serovar genomes, but the expression of fhese proteins is currently undefined. 

Figure 9.3 Inhibition of intimal hyperplasia by resveratrol in rabbits subjected to endothelial injury by denudation. Groups of eight New Zealand white rabbits, weighting 2.2 to 3.6 kg, were assigned randomly to control (untreated) (M), low (2 mg/kg/d) (L), and high dose (4 mg/kg/d) (H) resveratrol treatment, which was administered intragastrically for 5 weeks beginning 1 week before surgery. A 2-cm segment of injured iliac artery was excised, fixed in 4% paraformalin, embedded in paraffin, and sectioned at5-mm intervals from the proximal to the distal end. Representative sections were stained with hematoxylin/eosin. The external and internal elastic lamina were manually identified. Intimal proliferation index (IPI) was defined as the ratio of intimal area to [intimal+medial] area relative luminal area (RLA) was defined as the ratio of luminal area to [luminal+intimal+medial] area.

Many investigators have expressed their data in terms of F, the rate of diffusion, and have called this quantity the permeability of the material. O Neill and Goddard (7) found it more convenient to use the terms resistance and specific resistance. These are defined as the reciprocals of the permeability and the specific permeability respectively. The specific resistance is analogous to electrical specific resistance if the vapor pressure difference and the rate of diffusion are taken to be equivalent to potential difference and current in the electrical case. Diffusion resistances are additive (10), and the effect of each component of a complex system, in which the vapor diffuses through a number of consecutive laminae separated by layers of air, is at once apparent if the resistances of the individual components are known. 

Chert is defined here, following Folk (1980, p. 79), as a chemically precipitated sedimentary rock, essentially monomineralic and composed chiefly of microcrystalline and/or chalcedonic quartz, with subordinate megaquartz and minor amounts of impurities. Chalcedony, which consists of sheath-like bundles of thin, radiating fibers of SiOi, is rare in most Precambrian chert. Precambrian chert occurs as distinct beds or lenses, particularly in Archean rocks, as nodules or silicified laminae in carbonate rocks, or as a sihceous end-member, as granules or cements in iron formation. 

Irwin (40) gave an alternative formulation to fracture by considering the distribution or field of stresses around a crack in an elastic material. He proposed that such a distribution could be expressed as a function of a parameter K, known as the stress intensity factor, and he established that the fracture would occur when K exceeds a critical value characteristic of each material. Figure 14.33 shows a sharp crack of length 2a in an infinite lamina subjected to a tensile stress ct. The equations defining the local stresses an, a22 < 12 are (42)... 

The influence of the orientation of the laminae on the stiffness of the composite is illustrated in Figure 15.15b, where generic stress-strain curves for unidirectional cross-ply random laminates are shown. In the design of laminates it is necessary to define not only the orientation of the plies but also the stacking sequence, i.e., the order in which the plies are placed through the thickness. Figure 15.16 shows examples of symmetrical and non-symmetrical laminates. The most standard ply orientations are 0°,... 

Sometimes, there is a repeated stacking of the fabrics (or laminae within fabrics) in an ordered succession, reflecting changes in the composition of the drip waters. Two main types have been shown to occur on an annual scale (1) seasonal alternations of fabric and/or mineralogy defining... 

Biopsy specimens of PAH include constrictive lesions and complex lesions. Constrictive lesions comprise medial hypertrophy and intimal thickening. Medial hypertrophy is defined as the increase in both number and cross-sectional area of the SM cells lining the walls of the pre- and intra-acinar pulmonary arteries intimal thickening implies an increased number of fibroblasts in the thin layer between a SM cell and lamina propria of the blood vessel. These changes can be seen in both IPAH and pulmonary venous hypertension. In contrast, complex lesions are considered pathognomonic for PAH. The complex or plexiform lesion consists of focal proliferation of endothelial channels consisting of fibroblasts, SM cells, and connective tissue matrix. These lesions disrupt vascular vessel wall and serve as a nidus for in situ thrombosis. 

Perlecan, the major secreted proteoglycan in basal laminae, consists of a large multidomain core protein ( 400 kDa) with three or four specialized GAG chains. Both the protein and the GAG components of perlecan contribute to its ability to incorporate into and define the structure and function of basal laminae. Because of Its multiple domains with distinctive binding properties, perlecan can cross-link not only ECM components to one another but also certain cell-surface molecules to ECM components. 

Ninety percent of cancer deaths are caused by metastatic rather than primary tumors. Define metastasis. Explain the rationale for the following new cancer treatments (a) batima-stat, an inhibitor of matrix metalloproteinases and of the plasminogen activator receptor, (b) antibodies that block the function of integrins, integral membrane proteins that mediate attachment of cells to the basal laminae and extracellular matrices of various tissues, and (c) bisphosphonate, which inhibits the function of bone-digesting osteoclasts. 

Viscosity is a measure of a fluid s ability to resist motion when a shearing stress is applied. Considering a simple geometry (Fig. 1), the upper plate is caused to move with a velocity (v) relative to the lower plate. This velocity is due to the application of a shearing force F) per unit area. The layers of fluid contacting the plates are considered to move at the same velocities as the surface they contact i.e., the assumption is made that no slipping occurs at the walls. The fluid then behaves as a series of parallel layers, or lamina, whose velocities are proportional to their distance from the lower plate. The differentiation of velocity with respect to the distance (dv/dy) is defined as shear rate... 

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