Simple Shear and “Turbulence” of Polycrystals

We present an analogy between large plastic deformations of polycrystals and turbulent flows in fluid dynamics. The analogy explains a number of effects observed during large deformations, still unexplained in the language of plasticity theory. We also propose a phenomenological criteria characterizing the “turbulence” of polycrystals. Using this criteria, the paper shows that simple shear is possible only in materials whose representative elements admit a non-symmetric component of the corresponding velocity gradient. If this condition is not satisfied, the material only imitates simple shear replacing it with pure shear.