The description of anisotropic materials

It IS a safe generalisation to say that the properties of all solid materials —metals, ceramics, glasses and plastics—are dependent on their processing history. The temperature, method and speed of processing are each important variables. In any discussion of the effects of processing on properties, there is one important feature which simultaneously 

An isotropic material has the same properties in all directions. Properties such as refractive index and Young s modulus are independent of direction, and if we wish to refer the properties to a set of rectangular cartesian co-ordinates, we can rotate the axes to be in any orientation without any preferoice. For an anisotropic material, where the properties differ with direction, it is usually convenient to choose coordinate systems which coincide with axes of S3rmmetry if this is possible. The material is then described by its properties referred to these principal directions, which affords considerable simplification. 

The degree of complexity of this representation depends on the ten-sorial nature of the property. Properties which relate two vectors, such as dielectric constant k, which relates electric displacement D and electric field intensity , can be described by a symmetric second rank tensor with six independent components, viz. 

The components of the displacement Z), Dy, are then given in terms of the components of the electric field intensity , by the 

It is always possible to rotate the system of axes until the property is described by three components, the principal components Kt, k, K3. The second rank tensor then reduces to 

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