## Hydrostatic and Deviatoric Strain

85 The lagrangian and Eulerian linear strain tensors can each be split into spherical and deviator tensor as was the case for the stresses. Hence, if we define

then the components of the strain deviator E' are given by

We note that E' measures the change in shape of an element, while the spherical or hydrostatic strain iel represents the volume change.

rdros m-piola.nb m-piola.nb

The defc given by Thspe cífflrv

MatrixForm [Transpose [F] .n/detF]

ess tenscr is calculate the es ^disusing \$<C Jo h0 /we^t,aiô t tOlst = MatrixForm[Tfirst . {0, 1, 0>]

We note that this vector is in the same direction as t°e Cauchy stress vector, its magnitude is one fourth )f that of the

Cauchy stress vector, because the undeiormed area is 4 times that or the deiormed area

:or associated with the Second Piola-Kirchoff stress itainedlrom t=CST n i

We see that this pseudo stress vector is in a different direction from that of the Cauchy stress vector (and we note that

■ Pseudo—STres^vecioPassociated with the First Piola-Kirchoff stress tensor

■ First Piola-Kirshoff Stress Tensor

FT n

For a unit area in the deformed state in the direction, its undeformed area d^o nois given by d^o no = dtF

TfiF=Det[F] Figure 4.8: Mohr Circle for Strain
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### Responses

• christopher
How to calculate deviatoric strain?
8 years ago