A FE-Based Macro-Element for the Assessment of Masonry Structures: Linear Static, Vibration, and Non-Linear Cyclic Analyses

A Finite Element (FE) based macro–element is described for the mechanical response of masonry structures within different ranges of analysis. The macro–element is composed of discrete rigid quadrilateral FE plates whose adjoining interfaces are connected through FE trusses. It allows representing both elasticity and strength orthotropy, full material nonlinearity and damage through a scalar–based model. The possibility of coupling with a so–called FE^2 (multi–scale) strategy is also addressed. Validation of the macro–element is conducted within linear static, vibration, and cyclic (nonlinear) problems, in which both static and dynamic ranges are explored. Results are compared with those retrieved from traditional FE continuous models. Advantages are highlighted, as well as its robustness to cope with convergence issues and suitability to be applied within more general and larger–scale scenarios, such as the analysis of anisotropic materials subjected to static and dynamic loading. Formal details are given for its reproducibility by academics and practitioners—eventually within other FE platforms—as the improved running times may be of utmost importance in dynamic problems or highly nonlinear (material) quasi–static analysis.