While the Johnson-Cook model predicted the behavior of most materials in the Taylor tests, the model's prediction and test results for OFHC (oxygen free high conductivity) copper did not agree well.

In an approach seeking to improve on Johnson-Cook, Zerilli and Armstrong proposed a more sophisticated constitutive relation obtained through the use of dislocation dynamics.

The effects of strain hardening, strain-rate hardening and thermal softening (based on thermal activation analysis) have been incorporated into the formulation. The effect of grain size has also been included.

The relation has a relatively simple expression and should be applicable to a wide range of fcc (face centered cubic) materials.

A relation for iron has also been developed and is also applicable to other bcc (body centered cubic) materials.

An important point made by Zerilli and Armstrong is that each material structure type (fcc, bcc, hcp) will have its own constitutive behavior, dependent on the dislocation characteristics for that particular structure. For example, a stronger dependence of the plastic yield stress on temperature and strain rate is known to result for bcc metals as compared with fcc metals.

With this model, the yield stress varies depending on strain, strain rate and temperature.

The yield stress is given by:

For fcc metals

For bcc metals:

where

ε = effective plastic strain

= normalized effective plastic strain rate

T = temperature (degrees K)

The parameters Y₀, C₁, C₂, C₃, C₄, C₅ and n are material constants.

The plastic flow algorithm used in this model has an implicit strain rate correction option to reduce high frequency oscillations that are sometimes observed in the yield surface under high strain rates. The strain rate correction algorithm will be at the expense of increased CPU usage.

Custom results variables available for this model:

*Resultant value over shell/beam section.

**Temperature will be non-zero only if a specific heat capacity is defined.