A derivation of the Mehrabadi-Cowin equations

An alternative derivation to that given by Mehrabadi and Cowin (1978) is presented here for a pair of kinematic equations governing a certain class of flows in the plastic deformation of dilatant granular materials. This class has been described by Spencer (1981) as double shearing flows. In their derivation Mehrabadi and Cowin (1978), prior to presenting the equations relative to rectangular Cartesian coordinates, obtained an intermediate pair of equations relative to a non-orthogonal network of characteristic coordinates. The essential difference between the original and present derivation is that here, the flow rule, expressed relative to rotating, rectangular Cartesian coordinates, is transformed directly to obtain the kinematic equations relative to fixed rectangular Cartesian coordinate axes, without the need to obtain the characteristic equations.