eps(i)/dt is the way to get the strain rate components in LS-DYNA because eps(i) is derived from the time-centered strain rate multiplied with dt; see [1, eq. (18.7)]. Moreover, it is consistent with the central difference global time integration scheme [2, eq. (2.6.1.8)].
I don't know which rate-dependent material model you use. However, some of such models require a reference strain rate in addition to the related material constants. A set of constants is consistent if it has been determined from experiments at the reference strain rate.
Regards,
Daniel
[1] J. O. Hallquist. LS-DYNA Theory Manual. Livermore Software Technology Corporation, Livermore, California, USA, 2006
[2] D. J. Benson. Computational methods in Lagrangian and Eulerian hydrocodes. Computer Methods in Applied Mechanics and Engineering, 99(2-3):235–394, 1992
You may save the strain to a common block so you can get the strain from previous step, then by (eps_this_step - eps_previous_step)/dt, you can get the strain rate. Note that due to numerical noise, you may want to average the strain rate over several steps to get a more meaningful answer.
you may consider to use the equivalent strain rate. Based on the esp(1:6), the equivalent strain increment can be calculated. Next step is to divide the equivalent strain increment by using dt.