Metamaterial Inspired Electromagnetic Applications by Balamati Choudhury

Author:Balamati Choudhury
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

An example of representation of a typical tensor of rank 2 is given by

The first subscript of each tensor element keeps track of the plane the component acts on (described by its unit normal vector), while the second subscript keeps track of the direction. Each component represents a magnitude for that particular plane and direction.

Let be a force tensor (dyad) of an object. For example, consider forces inside an object. Imagine various surfaces inside an object whose area vector is pointed to various directions. For all such surfaces, there exists a force having components pointed to any of the basis vector directions. More clearly, represents a force in the direction of the basis vector ‘1’ whose surface is directed toward direction of basis vector ‘2.’

A second-order tensor defines an operation that transforms a vector to another vector. For example, tensor ‘A’ transforms a vector ‘a’ into another vector ‘b’ through a dot product as

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