A hyperbolic augmented elasto-plastic model for pressure-dependent yield

Abstract

A three-dimensional elasto-plastic model for the deformation and flow of granular materials which generalises the plastic potential model and contains an additional term analogous to that appearing in the double-shearing model is presented. It is shown that for planar flows the resulting system of first-order partial differential equations is hyperbolic. This is in distinct contrast to both the non-associated plastic potential and double-shearing models, which fail to be hyperbolic. The ill-posedness of the Cauchy problem for the planar double-shearing model is due to the presence of the rotation rate of the principal axes of stress while that of the non-associated plastic potential model is due to distinct quasi-static spatial stress and velocity characteristics. The present model attains well-posedness by replacing the planar rotation rate of the principal stress axes by the vector intrinsic spin of a Cosserat continuum and using it to ensure identical spatial stress and velocity characteristics. Flows in which the intrinsic spin vector is constant in both space and time correspond to flows in an ordinary continuum. The model governing such flows is embedded into a Cosserat model in such a way that the characteristic structure is preserved.