Discretised Continuum Approaches: From Continuum to Dis-Continuum

Prologue. The model of Heyman for Masonry as a solid fracturing continuum. In Chap. 1, the need for special computational strategies to analyse masonry structures is motivated. Most commercial structural software tools neglect contact, fracture and friction. Basically, there exist two conceptually simple ways to approach the problem while including these aspects. The first one is represented by Discrete Element Method (DEM) approaches, in the present book briefly described in Sect. 1.2.4 and fully illustrated in Chap. 5. The second one funds upon Heyman’s model and consists of a set of crude material restrictions catching at the macroscale the basic ingredients of masonry behaviour, allowing the use of Limit Analysis. Heyman’s theory can also lead to a variational formulation of the boundary value problem for masonry-like structures, described in Part I of this Chapter. This variational formulation naturally leads to two dual numerical strategies described in Part II of the present Chapter. A specific Chapter, Chap. 4, is dedicated to TNA, a striking example of a lower-bound limit-analysis-based method to assess vaulted masonry structures. With TNA, admissible equilibrium states correspond to compressive force networks within the structural geometry.