On blocks detection in unilateral masonry-like structures: a rigid-elastic displacement approach

In the present paper, a rigid block model for detection and identification of the cracks' pattern in a masonry-like structure subjected to dead loads and finite displacements is presented. The equilibrium problem is formulated by means of a suitable variational formulation for the boundary value problem of normal elastic no-tension material. Specifically, static equilibrium states of masonry-like structures are obtained through the linear conic optimisation of total potential energy. The independent variables of the optimisation problem are elastic strains and displacements, both assumed to be continuous. Indeed, the displacement and the strain fields are described in terms of nodal values through a FEM-like formulation and both of them are treated as independent variables of the optimisation problem. The study provides the basis for future developments in the field of mechanics and mechanisms of fracture. Two simple case studies are also discussed in order to tap the promising potential of the proposed approach.