17.11. POST1 and POST26 - Interpretation of Equivalent Strains

The equivalent strains for the elastic, plastic, creep and thermal strains are computed in postprocessing using the von Mises equation:

(17–144)

where:

ε_x, ε_y, etc. = appropriate component strain values

ν' = effective Poisson's ratio

The default effective Poisson's ratio for both POST1 and POST26 are:

The AVPRIN,,EFFNU command may be issued to override the above defaults (but it is intended to be used only for line elements, etc.).

The equivalent strain is output with the EQV or PRIN component label in POST1 (using the PRNSOL, PLNSOL, PDEF, or ETABLE commands) and in POST26 (using the ESOL command).

17.11.1. Physical Interpretation of Equivalent Strain

The von Mises equation is a measure of the “shear” strain in the material and does not account for the hydrostatic straining component. For example, strain values of ε_x = ε_y = ε_z = 0.001 yield an equivalent strain ε_eq = 0.0.

17.11.2. Elastic Strain

The equivalent elastic strain is related to the equivalent stress when ν' = ν (input as PRXY or NUXY on MP command) by:

(17–145)

where:

σ_eq = equivalent stress (output using SEQV)

= equivalent elastic strain (output using EPEL, EQV)

E = Young's modulus

Note that when ν' = 0 then the equivalent elastic strain is related via

(17–146)

where:

G = shear modulus

17.11.3. Plastic Strain

For plasticity, the accumulated effective plastic strain is defined by (see Equation 4–25 and Equation 4–42):

(17–147)

where:

= accumulated effective plastic strain (output using NL, EPEQ)

This can be related to (output using EPPL, EQV) only under proportional loading situations during the initial loading phase and only when ν' is set to 0.5.

17.11.4. Creep Strain

As with the plastic strains, to calculate the equivalent creep strain (EPCR, EQV), use ν' = 0.5.

17.11.5. Total Strain

The equivalent total strains in an analysis with plasticity, creep and thermal strain are:

(17–148)

(17–149)

where:

= equivalent total strain (output using EPTT, EQV)

= equivalent total mechanical strain (output using EPTO, EQV)

= equivalent thermal strain

For line elements, use an appropriate value of ν'. If > > , use ν' = 0.5. For other values, use an effective Poisson's ratio between n and 0.5. One method of estimating this is through:

(17–150)

This computation of equivalent total strain is only valid for proportional loading, and is approximately valid for monotonic loading.