Rigid blocks for masonry

This paper deals with masonry structures as composed by Normal Rigid No-Tension (NRNT) material. With the NRNT model the material is rigid in compression, but extensional deformations, allowed at zero energy price, can be either regular or singular; then extensional deformation can appear as either diffuse (smeared cracks) or concentrated (macroscopic cracks), and there is not any reason to prefer one upon another, on an energy ground. The fact that rigid block deformation seems to be the preferred failure mode for real masonry structures stems from mechanical characteristics, such as toughness and cohesion, that are not inherent to the simplified NRNT continuum model. So, it is interesting to see if rigid block mechanisms can arise naturally in solving the equilibrium problem, and if there is any legitimate way to force rigid block mechanisms over diffuse cracking. We formulate the equilibrium problem as an energy minimum search and propose two methods for approximating the solution. With the first one we minimize the energy in the set of piecewise-rigid (PR) displacements. With the second method, we explore the possibility to restrict the search of the minimum to continuous (C°) displacement fields, by adopting some classical Finite Element (FE) approximation.