From engineering to true strain, true stress

First of all, you may check that your experimental data from a uniaxial tension test is expressed in terms of true stress vs. true strain, not engineering stress or strain.

True strain = ln(1 + engineering strain) where ln designates the natural log

True stress = (engineering stress) * exp(true strain) = (engineering stress) * (1 + engineering strain) where exp(true strain) is 2.71 raised to the power of (true strain).

Be aware that experimental data always includes some degree of error and thus tends to be somewhat noisy or erratic. When using *MAT_24, one should input a smoothed stress-strain curve utilizing a minimal number of points. Input of noisy experimental data may cause spurious behavior, particularly in the case of the default, 3-iteration plane stress plasticity algorithm for shells. Full iterative plasticity can be invoked for shells, at greater expense, for material models 3, 18, 19, and 24 by setting MITER=2 in *CONTROL_SHELL.

The effective plastic strain values input in defining a stress vs. effective plastic strain curve in a LS-DYNA plasticity model should be the residual true strains after unloading elastically. True stress is input directly for the stress values.

Using experimental data from a true stress vs. true strain curve ...

effective plastic strain (input value) = total true strain - true stress/E

Note that as the stress value increases, the recoverable strain (true stress/E) increases as well. For metals, E is very large compared to the yield stress so it's fairly common practice in the case of metals to just subtract off a constant value equal to the strain at initial yield from all subsequent strain values. For plastics/polymers, you probably should consider the increase in recoverable strain as stresses increase (since the elastic component of strain may be quite large). In any case, the first plastic strain value should be input as zero and the first stress value should be the initial yield stress.

In the case where the user elects to input only an initial yield stress SIGY and the tangent modulus Etan in lieu of a true stress vs. effective plastic strain curve (in *MAT_PIECEWISE_LINEAR_PLASTICITY),

Etan = (Eh * E)/(Eh + E) where Eh = (true stress - SIGY)/(true strain - true stress/E)

Eh = (Etan * E)/(E - Etan) if E > Etan

E should not be less than Etan where Etan is computed from E and Ep, where Ep is the initial slope of the piecewise linear stress vs. epspl curve (presumably this is the steepest portion of the curve). In *MAT_24, this is exactly the input check that is made if LCSS=0 and cards 3 and 4 are blank (E must be greater than ETAN or else you get a fatal error).

Actually, this condition of E > Etan is ALWAYS met if a stress vs. epspl curve is given. For example, if Ep = 3253 and E were set to an extremely low value, say 10, Etan is then equal to Ep*E/(Ep + E) = 9.97. If cards 3 and 4 are used to define the curve, the job will stop due to an improper though conservative check of E against Ep. You can always bypass this check by using LCSS instead of cards 3 and 4.

jpd 5/2002