A continuum model of close packing granular materials for the study of rock filled gabions. (15th March 2020) - Brocato, Maurizio
Abstract: We propose a model for the study of rock filled gabions, based on the theory of continua with microstructure, where the interlocking of stones through contacts figures explicitly. In this model, each stone is partly locked by its first neighbours, appearing as a continuous deformable box. While stones are material items, as such endowed with inertia, boxes are configurational features, as e.g., crack tips or phase boundaries. Two kind of internal actions are then included in the model: (1) material actions that represent the internal forces and moments arising in the boxing process and (2) configurational actions that possibly drive boxes to change shape or make contacts within them be updated. Following the theory of continua with microstructures, each material and configurational element of the continuum is endowed with geometrical properties, working with respect to the above mentioned internal actions. In order to reduce the complexity of this geometry (and of the ensuing mathematical problem), preserving nonetheless a sufficiently accurate description of the boxing process, we will consider stones and boxes having a one-to-one permanent connection, represented by a symmetric traceless tensor, akin to a fabric tensor. The set of equilibrium equations that define the mechanical problem is then divided into two groups: (1) balance of material momentum and moment of momentum, expressed in the usual vectorial space of forces and (2) balance of configurational dynamical entities, expressed in the space of second order tensors. The dissipative and non-dissipative parts of the stresses are then related to a free energy potential and to a dissipation potential, within the framework of rate independent processes.