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Isotropic area deformations

If area changes are performed in an anisotropic way, for example in trough experiments, the theoretical model has to take into account the lateral transport of adsorbed molecules (Lucassen Giles 1975, Dimitrov et al. 1978, Kretzschmar K6nig 1981). Assuming isotropic area deformations, the diffusional flux at the interface is given by... [Pg.208]

Assuming isotropic area deformations, the diffusional flux at the interface is given by... [Pg.330]

When the probe makes contact with the film, it generates a radial stress field around the point of contact. If the film is isotropic, it deforms in a uniform ring around the probe, as shown in Fig. 8.11 a). If the film is oriented, it deforms in a non-uniform manner. When the film is mildly oriented, the deformation area becomes ellipsoidal, as we see in Fig. 8.11 b), with its long axis... [Pg.168]

The software driven apparatus allows different types of area changes step and ramp type, square pulse and trapezoidal as well as sinusoidal area deformations. The construction ensures that area changes are almost isotropic. Area changes used in transient and harmonic relaxation experiments are of the order of 1 to 5%. The surface tension response measured via the Wilhelmy balance has an accuracy of better than 0.1 mN/m. [Pg.220]

E. Winkler, F. Grashof, H. Hertz,8 etc., have studied the stresses which are set up when two elastic isotropic bodies are in contact over a portion of their surface, when the surfaces of contact are perfectly smooth, and when the press, exerted between the surfaces is normal to the plane of contact. H. Hertz showed that there is a definite point in such a surface representing the hardness defined as the strength of a body relative to the kind of deformation which corresponds to contact with a circular surface of press. and that the hardness of a body may be measured by the normal press, per unit area which must act at the centre of a circular surface of press, in order that in some point of the body the stress may first reach the limit consistent with perfect elasticity. If H be the hardness of a body in contact with another body of a greater hardness than H, then for a circular surface of pressure of diameter d press. p radius of curvature of the line p and the modulus of penetration E,... [Pg.453]

Figure 1. Uniaxial Extension of a Non-Homogeneous Sample. The figure shows simulation results for uniaxial extension of an initially (a) square sample whose orientation is primarily left-to-right, except for the central cross-shaped region, which is isotropic. After 25% stretching (b), the cross-shaped region is deformed more than the surrounding tissue, with roughly a 5% greater increase in area. Figure 1. Uniaxial Extension of a Non-Homogeneous Sample. The figure shows simulation results for uniaxial extension of an initially (a) square sample whose orientation is primarily left-to-right, except for the central cross-shaped region, which is isotropic. After 25% stretching (b), the cross-shaped region is deformed more than the surrounding tissue, with roughly a 5% greater increase in area.
The described principle of equal force (stress) and added deformations (strains) equally applies to parallel layers of any kind, provided that their structure is isotropic. However, if any of the layers in the array is incompressible and softer than the rest, then it will expand laterally upon the force application. This is a familiar experience. When a sandwich or a layered cake is compressed, the filling sometimes leaks out from the sides, as shovm schematically in Figure 10.10. For such a situation. Equations (10.7) or (10.8) will not be an appropriate model. However, because the cellular layers retain their cross-sectional area, and because the free p>art of the expanded filling does not transmit any stress (theoretically), the stress-strain relationship of the array can still be calculated by accounting for the exuded material. [Pg.180]

The response of an isotropic, homogeneous solid to a force is expressed in terms of the elastic constants or elastic moduli. [Unfortunately, a standard set of symbols for these constants is not in use.] Four elastic constants are frequently defined but, as they are interrelated, the elastic properties of a solid can be defined in terms of any two. They are most conveniently defined with respect to the stress, which is the force per unit area applied to the body, and the strain, which is the deformation of the body produced by the force. [Pg.543]

The membrane deformation is calculated from observed macroscopic changes in cell geometry, usually with the use of simple geometric shapes to approximate the cell shape. The membrane force resultants are calculated from force balance relationships. For example, in the determination of the area expansivity modulus of the red cell membrane or the cortical tension in neutrophils, the force resultants in the plane of the membrane of the red cell or the cortex of the white cell are isotropic. In this case, as long as the membrane surface of the cell does not stick to the pipette, the membrane force resultant can be calculated from the law of Laplace ... [Pg.1019]

The otoliths are an overdamped second-order system whose structure is shown in Figure 64.1a. In this model the otoconial layer is assumed to be rigid and nondeformable, the gel layer is a deformable layer of isotropic viscoelastic material, and the fluid endolymph is assumed to be Newtonian fluid. A small element of the layered structure with surface area dA is cut from the surface and a vertical view of this surface element, of width Ax, is shown in Figure 64.1b. To evaluate the forces that are present, free body diagrams are constructed of each elemental layer of the small differential strip. See the nomenclature table for a description of all variables used in the following formulas (for derivation details see Grant et al., 1984 and 1991). [Pg.1078]

The second contribution to the surface energy is new because it is based on an extension of the atomic distances in the surface area by a force called surface stress. The symbol used for the surface stress in this book is T as in the review of Linford. The surface stress is a tensor with the tensor components T, T, T, and T. The tensor is only independent in its direction for an isotropic sohd. The surface stress causes an elastic deformation of the surface described by the surface strain tensor e. ... [Pg.113]

Figure 1 Optical micrograph of a U-shaped hinge after 100 bending cycles, using crossed polars. The highly oriented layers appear dark, the isotropic central layer is bright. One can see the small deformation area not in the middle of the hinge but near to the gate (arrows indicate). The flow direction of the polymer melt is from the right to the left side. Figure 1 Optical micrograph of a U-shaped hinge after 100 bending cycles, using crossed polars. The highly oriented layers appear dark, the isotropic central layer is bright. One can see the small deformation area not in the middle of the hinge but near to the gate (arrows indicate). The flow direction of the polymer melt is from the right to the left side.
Simple Extension of Swollen Networks. The force required to deform an elastomeric sample, from state 2 to state 3 in Figure 13, is given by equation (57), in which a =L/L is the extension ratio for the isotropic swollen state relative to the deformed swollen state. The ratio VofV is the volume fraction of polymer in the swollen system, and Aq is the cross-sectional area of the dry sample, which is generally measured before the experiment. The area of the swollen sample is given by... [Pg.2333]

Expansion work does not require a cylinder-and-piston device. Suppose the system is an isotropie fluid or solid phase, and various portions of its boundary undergo displaeements in different directions. Figure 3.5 shows an example of compression in a system of arbitrary shape. The deformation is eonsidered to be carried out slowly, so that the pressure p of the phase remains uniform. Consider the surface element t of the boundary, with area /4s,T, indicated in the figure by a short thick curve. Beeause the phase is isotropic, the force = pA z exerted by the system pressure on the surroundings is perpendicular to this surface element that is, there is no shearing force. The force exerted by the... [Pg.73]

If the surface energy density per unit deformed surface area remains constant, then the surface stress is an isotropic second rank tensor with components numerically equal to 11. On the other hand, if the surface energy density per unit undeformed surface area remains constant, the surface stress vanishes. [Pg.29]

For spheres of the same isotropic elastic material with plane strain modulus E and the same undeformed radius R, the deformed contact area is flat and its boundary is circular due to the symmetry of the configuration. According to the Hertz point of view, the normal stress distribution predicted for the contact area z = 0,0[Pg.645]

Over recent years a completely different approach has been adopted by Hu, Day, Stanford and Young [66-69], who have shown that, through the synthesis of specially designed copolymers, it is possible to prepare isotropic polymers for which the deformation can be followed using Raman spectroscopy. They have demonstrated that such materials can be used for the study of polymer surface and interface deformation [68,69] and their work in this area is reviewed below. [Pg.214]

If an compressive normal force Fn S acting on a sojl contact of two isotropic, stiff, linear elastic, mono-disperse spherical particles the previous contact point is deformed to a small contact area and the adhesion force between these two partners is increasing, see Rumpf et al. [22] and Molerus [8]. [Pg.74]

If the dimensional changes are considered as produced by a uniform swelling superposed on a contraction in area, the contraction can be interpreted as recovery of a frozen-in strain according to this view, the film behaves as though it were an isotropic structure which had been stretched uniformly in all directions in its own plane, the deformation being restrained from recovery until released by the swelling process,... [Pg.67]

Polarizing light microscopy employs crossed polarizers to view the sample. With isotropic specimens, the field of view is dark, while anisotropic, birefringent samples or areas of a sample will appear bright. Polarizing microscopy is employed to view spherulitic structure [66-68] and deformation morphologies (crazes, shear banding) [69] in polymer blends. Samples for... [Pg.271]


See other pages where Isotropic area deformations is mentioned: [Pg.161]    [Pg.45]    [Pg.285]    [Pg.108]    [Pg.255]    [Pg.3]    [Pg.354]    [Pg.485]    [Pg.67]    [Pg.470]    [Pg.336]    [Pg.90]    [Pg.113]    [Pg.203]    [Pg.99]    [Pg.105]    [Pg.161]    [Pg.745]    [Pg.169]    [Pg.55]    [Pg.33]    [Pg.271]    [Pg.193]    [Pg.122]    [Pg.295]   
See also in sourсe #XX -- [ Pg.208 ]

See also in sourсe #XX -- [ Pg.330 ]




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