Anisotropic deformations

Sumita, J. et al., Anisotropic deformation effect on the fracture of core components made of two-dimensional C/C composite, Key Engineering Materials, Trans Tech Publications Ltd., Switzerland, 143,2005. 

The two principle modes of the magnetostriction (A -° and As or Xy-2) introduced above are illustrated in fig. 2. With respect to the non-magnetic fictitious state, a spherical, isotropic sample exhibits a relative volume change AV/V = A" 0, when it becomes magnetic. In addition, when one forces the moments to be directed along an applied magnetic field B, an anisotropic deformation is induced, which transfers the sphere into an ellipsoid with the same volume. 

The higher order terms are relevant for the case of anisotropic deformations [25]. The second term, [02(1,7)], is a two-body term which accounts for the increase in energy when N bonds are compressed below their equilibrium value. This effect is also modeled with an equivalent crystal, whose lattice parameter is obtained by solving a perturbation equation given by... 

For anisotropic deformation, it is important to realize that the virtual chains in component directions i = x,y,z have different numbers of... 

Swelling of network rubbers by solvent liquids represents an isotropic deformation. Stretching a swollen rubber network superimposes an anisotropic deformation. The two deformations may be combined as described below to obtain an estimate of the force (or modulus) required to deform a swollen rubber compared to that for unswollen rubber. The... 

The formation of the LC-phase causes an anisotropic deformation of the network even without action of mechanical forces. The degree of deformation depends on the degree of order of the LC-phase. 

Emphasis should be laid on the very intimate relation apparantly existing between the phenomena of swelling and deformation in systems of this kind. Mechanical extension or compression involve an anisotropic deformation of the very same network structure, whereby changes in the distances between the junction points, bound up with stretching or contraction of the molecular chains extending between them, occur too. Swelling may be compared with a threedimensional isotropic extension. 

It is to be noted, that the effects of anisotropic deformation and anisotropic swelling run parallel. We shall see later, that and why the two factors are very intimately related in macromolecular systems ( 9c. 2). 

FIGURE 2.20 Microscopic stress versus strain relation. Elastic pressure is depicted as a function of the swelling parameter r] for the three scenarios of pore wall deformation, discussed in this section. They correspond to isotropic deformation (Equation 2.33), anisotropic deformation (Equation 2.34), and elongation (Equation 2.35). 

Gotoh T. and Tanaka K. Photoinduced surface deformations in ion-conducting Ag-As-S glasses. II. Anisotropic deformations produced by large light spots,/. App/. Phys., 89, 4703-4706 C2001b). 

Tanaka K., Visible anisotropic deformation of chalcogenide glass by illumination of linearly polarized light, App/. Phys. Express, 1, 012006 (2008). 

Tanaka K. and Asao H., Photoinduced anisotropic deformation in AS2S3 glass, Jpn.J.AppI. Phys., 45,1668-1674 (2006). 

Tanaka K., Saitoh A., and Terakado N., Anomalous anisotropic deformations of AS2S3 flakes induced by linearly-polarized bandgap illumination./ Non-Cryst. Solids, 355,1828-1831 (2009a). 

---