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By the way, this is where you can make the difference between strain rate and gradient of velocity. Your sentence is formaly wrong : updating relative velocities needs the gradient of velocity (obviously!), not the strain rate tensor. Strain rate, being the symmetric part of velGrad, is not enough to describe the transformations of the period. You will not see any difference in the usual triaxial path, but you will in simple shear.the usage of the strain rate of loading to update relative velocities...
Bruno
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