Discrete element slip model of plasticity

A two-dimensional domain under plane-stress conditions is considered. The admitted external loading comprises a unidirectional uniform body force and distributed forces along the boundary. By considering a discrete element slip model and applying the principle of virtual work, a comprehensive set of equilibrium equations purely in terms of the average shear stress along edges of a triangulated mesh in derived. Plastic collapse by incompressible flow due to shear failure at a limit stress can thereby be analyzed. The collapse mechanisms therein would contain tangentially discontinuous velocity fields. The coefficient of each shear stress term in the equilibrium equations is the sum of cotangents of two vertex angles in the mesh, whereas the coefficient of each boundary normal stress term is plus or minus unity. The number of internal nodes, boundary nodes and restrained boundary edges, together with the degree of connectivity of the domain, are adopted as primary quantifiers of the size of the numerical problem.