Stationary shock in cohesive-frictional materials

This paper is concerned with the theoretical analysis of a stationary shock in cohesive-frictional plastic materials. The shock is defined as a thin layer of localized deformation through which material particles travel during plastic flow, as opposed to a shear band where material particles neither enter nor leave the layer. Mathematically, the shock is regarded as a strong discontinuity in velocity and density. Shocks may occur in cohesive-frictional materials in the problem of indentation of soils and rocks, flow of granular materials in bins and hoppers, rock cutting, etc. In the paper we formulate equations on the stationary shock in rigid-plastic materials with or without hardening or softening. The analysis incorporates the effect of inertia of material crossing the shock. The solution and the necessary condition for the existence of a shock are studied under the assumption that the same flow rule is valid for the material within and the material outside the shock. Three regimes of solution are identified, depending on the ratio of specific kinetic energy and cohesion. Using particular forms of constitutive equations it is demonstrated that a stationary shock cannot exist without some hardening of the material. An example of application of the theoretical framework developed to the problem of wedge indentation is considered for one type of material behavior.