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# 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:

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, Em, ?m is essentially a scalar (tensor of order zero) having only magnitude with all directions principal. It is sometimes called the spherical component. The mean stress, ?m, is hydrostatic pressure if neg-ative, or suction if positive, and causes only volume change, 3Em, per unit volume. The deviatoric component is just the opposite in that it causes only distortion or shear with no volume change. The invariants of the deviatoric tensors are:

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 |