Anisotropic material definition

Compare the transformed orthotropic compliances in Equation (2.88) with the anisotropic compliances in terms of engineering constants in Equation (2.91). Obviously an apparenf shear-extension coupling coefficient results when an orthotropic lamina is stressed in non-principal material coordinates. Redesignate the coordinates 1 and 2 in Equation (2.90) as X and y because, by definition, an anisotropic material has no principal material directions. Then, substitute the redesignated Sy from Equation (2.91) in Equation (2.88) along with the orthotropic compliances in Equation (2.62). Finally, the apparent engineering constants for an orthotropic iamina that is stressed in non-principal x-y coordinates are... 

Identity Equation (2.97) by interpreting Equation (2.88) using Equation (2.90) as well as Equations (2.91) and (2.62). Explain tbe key logical step that enables you to use both Equations (2.90) and (2.91) for anisotropic materials and Equations (2.62) and (2.88) for orthotropic materials in this problem. That Is, in what way can we interpret a material as satistying both definitions ot a material ... 

Similar invariance concepts for anisotropic materials were also developed by Tsai and Pagano [2-7]. For anisotropy, the following definitions... 

Qi are for anisotropic materials. Qy for orthotropic materials are obtained by deleting Ug and Uy from the definitions of Qy. 

Refractive index is the ratio of electromagnetic radiation in vacuo to the phase velocity of electromagnetic radiation of a specified frequency in the medium (ISO definition). The definition implies that the refractive index is always greater than unity and that it is dimensionless. For anisotropic materials the state of polarization of the light and its direction must be defined relative to reference axis in the sample. 

By definition, a magnetic moment of substance per unit volume is magnetization M = xH. For an anisotropic material, the magnetization vector components are Ma = and the contribution to the fi-ee energy density of the mesophase from the magnetic field is given by [1] ... 

The field that generates these eddy currents is, by its nature, anisotropic, i e the eddy current signal response is directionally dependent on probe orientation. This can be used advantageously if one bears in mind that the corroded material one aims to detect usually displays random peaks and valleys, while man-made edges have a definite orientation. 

To create micromachines, films that have been deposited must be patterned and etched to reveal the desired structures. Often, it is important to etch these structures with vertical sidewalls (anisotropic etching). In this case, most pattern transfer operations (lithography and etch) are carried out using plasma etching. Conceptually, this process is the reverse of deposition. The etching process consists of exposure of the patterned and masked substrate to a low-pressure plasma. The reactive species and ions preferentially etch those areas that are not masked, resulting in the definition of features on the surface. The key to plasma etching is that the products of the reaction of the activated gas and the material to be etched must be volatile (see e.g.. Ref ). 

The theory outlined above is rigorous only for infinitesimal elastic deformation. Creep of polymeric materials is explicitly concerned with time dependence and implicitly with finite strains and therefore nonlinear behaviour. The nature of the non-linear behaviour is complex and varies not only from material to material but also with direction within a given sample of material, i.e. the non-linearity of behaviour is anisotropic. It is found, therefore, that on a particular definition of strain the behaviour of a sample may appear to be linear in one direction and significantly non-linear in another. Such a phenomenon is demonstrated in results presented below. 

Most polycrystalline solids are considered to be isotropic, where, by definition, the material properties are independent of direction. Such materials have only two independent variables (that is elastic constants) in matrix (7.3), as opposed to the 21 elastic constants in the general anisotropic case. The two elastic constants are the Young modulus E and the Poisson ratio v. The alternative elastic constants bulk modulus B and shear modulus /< can also be used. For isotropic materials, n and B can be found from E and t by a set of equations, and on the contrary. 

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