Dear all
I’m studying hypoplastic constitutive law from beginning concepts
I traced concepts successfully until i faced **rate independent topic**
i read this topic in the prof. Wolfgangs paper (hypoplasticity for beginners)
he said that “Rateindependence means that the gradient of the curve (stiffness) does not depend on the strain rate, Thus the stress rate must be precisely twice as large for a double strain rate” and in the fallowing he said that “the constitutive law may not have terms like (strain rate^2) (strain rate square )”
as you know the hypoplastic constitutive law is nonlinear in strain rate
my question is that how hypoplastic constitutive law can fulfill the nonlinearity (in strainrate) with no term like (strain rate^2)
Hypoplastic rate independent and nonlinearity
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Dear Sobhan, hypo equation is defined as stressrate=L:strainrate * Nstrainrate. Here, strainrate is Euclidean norm of strainrate, that is sqrt(strainrate:strainrate). You see that the equation is nonlinear in strainrate (if strainrate changes direction, stressrate changes direction differently as the term with N only quantifies strainrate size, not direction). You also see that actually, units of strainrate are still 1/time, as there is sqrt(strainrate^2) involved, thus it is consistent with comment by prof. Wolffersdorff which you cited. I suggest to have a loom into my book “Modelling of Soil Behaviour with Hypoplasticity”, where fundamentals of hypoplasticity are explained in (hopefully) clear way. Regards David
thank you so much!