Modeling of amorphous solids by polyclustering technique

Abstract
The paper presents certain aspects of theoretical modeling of amorphous solids with at least some degree of local order. The local short-range order versus the long-range disorder of amorphous structure is described in terms of Voronoi polyhedra, so that the resulting topological tessellations form groups of polyclusters. Consequently, the polyclusters can be considered as individual elements of micromorphic continua. Master equations of micromorphic continua are then perceived as a fundamental set of field equations that are needed for further theoretical development of the model. The semi-discrete nature of field variables describing the kinematics of deformation in polyclusters leads to the natural choice of a pair potential function for modeling a short-range order. Finally, the problem of consistent transition from micro to macro scale is addressed together with the question of a proper choice of a spatial averaging technique.