Alternative Definitions of Micro–to–Macro Transitions in Particle Aggregates of Granular Materials

An alternative approach to the modelling of the overall macroscopic response of granular materials is presented based on micro–macro transitions. A homogenized macro–continuum is considered with locally attached granular microstructures. The new developments include a consistent transfer of micro–macro transitions from continuous to particle microstructures with a new overall macro–stress definition. Secondly, a new class of boundary conditions for displacements/ rotations on prescribed boundary–frame particles is presented that yields upper and lower bounds with regard to the aggregate stiffness. Thirdly, a unified implementation of the displacement/ rotation boundary constraints by a penalty method is developed that proves to be a convenient computational tool in explicit codes.