Ill‐posedness in three‐dimensional plastic flow

This paper examines partial differential equations for frictional materials flowing via plastic yield, including the equations given by the Critical State Theory of Soil Mechanics. In particular, the material density is considered as a dependent variable. In previous work we demonstrated that two‐dimensional plastic flow may be ill posed due to an instability along two rays in Fourier transform space. In this paper, we show that in three dimensions the equations are linearly well posed provided all three strain rates are nonzero.