Effective plastic strain is a
monotonically increasing scalar value which is calculated incrementally as a function of
(Dp)ij, the plastic component of the rate of deformation tensor. In tensorial notation,
this is expressed as...
epspl = integral over time of (depspl) = integral [ sqrt( 2/3 (Dp)ij (Dp)ij ) ] dt
(See the equation for effective plastic strain in the description of Material Model 3 in
the LS-DYNA Theory Manual. To understand the notation, look under the heading of "Summation Convention" in this page...
http://www.brown.edu/Departments/Engineering/Courses/En221/Notes/Index_notation/Index_notation.htm or
see http://ftp.lstc.com/anonymous/outgoing/support/FAQ_docs/tensor_notation.png for a screenshot.)
Effective plastic strain grows whenever the material is actively yielding, i.e.,
whenever the state of stress is on the yield surface.
In contrast, the tensorial strain values, written by LS-DYNA when
STRFLG is set to 1 in *database_extent_binary, are not necessarily
monotonically increasing as they reflect the current, total (elastic + plastic)
state of deformation. To fringe the tensorial strains in LS-PrePost, click
Fcomp > Strain.
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RE: Effective strain
Effective strain, expressed in tensorial notation, is sqrt[ 2/3 (epsdev)ij (epsdev)ij ]
where epsdev are deviatoric strains.
This is NOT the same thing as effective plastic strain.
The effective strain calculation in LS-PrePost is as follows:
tensor strains sx,sy,sz,sxy,syz,szx
mean strain p=(sx+sy+sz)/3
deviatoric strains dx = sx - p, dy = sy - p, dz = sz - p
aa = sxy^2 + syz^2 + sxz^2 - dx * dy - dy * dz - dx * dz
effective strain es=sqrt(4*abs(aa)/3)
es = sqrt(2.0*(sx^2+sy^2+sz^2)/3.0 + (sxy^2+syz^2+szx^2)/3.0)
gives a value which is only ~2% less (not sure why the difference).
In terms of principal strains it is: es = sqrt(2.0*(s1^2+s2^2+s3^2)/3.0)
Again, this gives a value which is only ~2% less.
See http://ftp.lstc.com/anonymous/outgoing/support/FAQ/effstrain.tar for a test case for
shells which includes a spreadsheet.
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For a simple, 1-element illustration of various strain measures,
run http://ftp.lstc.com/anonymous/outgoing/support/FAQ_kw/mat24.cycle.k and then overlay time histories of
z-strain, effective strain, and effective plastic strain.
Other measures of strain can be fringed in LS-PrePost but these are calculated by
LS-PrePost from nodal coordinates, e.g.,
Fcomp > Infin (infinitesimal or engineering strain)
Fcomp > Green
Fcomp > Almansi
Be aware the infinitesimal strain is affected by rotation of the element as illustrated by
ftp://ftp.lstc.com/outgoing/support/FAQ_kw/spinup.bar.expl_dr.k.
Strain measures are addressed in
http://en.wikipedia.org/wiki/Deformation_(mechanics)
http://en.wikipedia.org/wiki/Finite_strain_theory#Finite_strain_tensors
http://en.wikipedia.org/wiki/Infinitesimal_strain_theory
For definition of effective stress, aka von Mises stress, try the following links:
http://en.wikipedia.org/wiki/Von_Mises_yield_criterion
http://www.continuummechanics.org/cm/vonmisesstress.html
http://en.wikipedia.org/wiki/T-criterion
In tensorial notation, effective stress is sqrt[ 3/2 (sij)(sij) ]
where sij are deviatoric stresses.
sigvm = 1/sqrt(2) * sqrt[ (sigx-sigy)^2 + (sigy-sigz)^2 + (sigz-sigx)^2 + 6*sigxy^2 + 6*sigyz^2 + 6*sigzx^2 ]
or
sigvm = 1/sqrt(2) * sqrt((sig1-sig2)^2 + (sig2-sig3)^2 + (sig3-sig1)^2)