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 mpiola.nb mpiola.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 PiolaKirchoff 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 PiolaKirchoff stress tensor
■ First PiolaKirshoff 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]
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christopher8 years ago
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