As we have seen in previews Section , any symmetric tensor can be split into isotro-pic and deviatoric components as follows:

**Isotropic and
Deviatoric Components**

As we have seen in previews Section , any symmetric tensor can be split into isotro-pic and deviatoric
components as follows:

a)
*For strain*:

The isotropic component, *E** _{m}*,
?

This uncoupling of the tensor into
isotropic and deviatoric parts will turn out to be a fundamental physical
reality that is reflected both in the way materials behave under load, and how
the stress, strain, and displacements 'flow' through a body. It also turns out
that there is a particular orientation of axes (of viewing the tensor) where,
in fact, this fundamental uncoupling occurs naturally and the tensor components
become the invariants them-selves. This is the so-called octahedral state.

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Civil : Principles of Solid Mechanics : Strain and Stress : Isotropic and Deviatoric Components |

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