Stresses in bulk solids in wedge hoppers: A flexible formulation of the co-ordinate specific, Lame–Maxwell equations for circular arc, principal stress systems

A 2-D model of stress distribution within bulk solids, with circular arc principal stress orientation, in a wedge hopper was developed in a previous paper [Matchett, OʹNeill, & Shaw, Stress distributions in 2-dimensional, wedge hoppers with circular arc stress orientation — a co-ordinate-specific Lamé–Maxwell model, Powder Technology, 187(2008) 298–306]. This model worked in an orthogonal, curvilinear co-ordinate system co-incident with the principal stress trajectories: (x − ψo) space. aper presents an equivalent model in (x − ε) space. This allows backward numerical integration of the force balance equations, enabling surface and wall boundary conditions to be modelled. This was not possible in the original model. uations are first-order, and boundary conditions can only be specified at single surfaces. Thus, if a stable, cohesive arch is proposed, the surface overpressure is determined by the model. Calculated overpressures have reasonable physical values. esent model was integrated backwards from the surface downwards and it was found that the integration was very sensitive to the surface overpressure stresses. se, wall boundary conditions were specified with backwards integration in ε. nimum outlet for flow was calculated from the model and compared with the experimental data of Berry et al. Wall normal stresses in a wedge hopper from Schulze and Schwedes were also compared to model predictions. In both cases there was reasonable agreement between measurements and model predictions.