Representation Surfaces for Physical Properties of Materials by Manuel Laso & Nieves Jimeno

Author:Manuel Laso & Nieves Jimeno
Language: eng
Format: epub
ISBN: 9783030408701
Publisher: Springer International Publishing

© Springer Nature Switzerland AG 2020

M. Laso, N. JimenoRepresentation Surfaces for Physical Properties of MaterialsEngineering Materialshttps://doi.org/10.1007/978-3-030-40870-1_6

6. Symmetric Second Rank Properties

Manuel Laso1 and Nieves Jimeno1

(1)Universidad Politécnica de Madrid ETSI Industriales, Madrid, Spain

Manuel Laso (Corresponding author)

Email: [email protected]

Nieves Jimeno

Email: [email protected]

In the previous chapter RSs were first introduced for the polar classes in their conventional axes, and then in an axes-free setting. We saw that a single type of geometrical object, the oriented sphere, was enough to construct the RS for all crystallographic and limit classes. Their RSs exclusively differed in their orientation with respect to the standard conventional axes.

In this section we will start from the more general axes-free point of view, taking mechanical stress as a representative example of symmetric second rank tensors. Although a field tensor and not a matter tensor, mechanical stress is useful because it is quite familiar and general, in the sense that all its eigenvalues can be positive, negative or zero.

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