Double-shearing theory applied to instability and strain localization in granular materials

Abstract

An account is given of the non-dilatant double-shearing theory of plane flow of granular materials, and it is shown that the theory may be formulated as a special form of hypoplasticity theory. It is shown that according to this theory, simple shearing flows may be supported by a time-independent stress field, but that this solution is unstable. An alternative solution in which the stress in time-dependent is also derived, and shear flow takes place under decreasing shear stress. The strain localization theory of Rudnicki and Rice is applied in conjunction with the double-shearing theory, and it is shown that the theory admits bifurcations in which shear bands form on planes that coincide with the shear plane. Similarly, in pure shear, there exists an unstable solution with time-independent stress, and a solution with time-dependent stress in which the compressive load falls as the deformation increases, and shear bands may form at surfaces on which, according to the Coulomb criterion, the critical shear stress is mobilized. The double-shearing theory for axially symmetric flow is summarized, and applied to compression of a circular cylinder. Again there is an unstable constant stress solution, a time-dependent stress solution in which the axial pressure decreases as the compression of the cylinder increases, and conical shear bands may form on conical surfaces on which the critical shear stress is mobilized.