Nonlinear static analysis of masonry structures with mortar joints and cracking units by optimization-based rigid block models

A rigid block model with elasto-plastic softening interfaces is developed for nonlinear static analysis of masonry structures subject to monotonic loading. Cracking, crushing, and shear failures are taken into account at interfaces, following a simple micro-modeling approach. An optimization-based formulation is used for the solution of the equation systems governing the behavior of the rigid block assemblage. A simple incremental solution procedure is implemented to take into account the material softening behavior and the effects of large displacements on equilibrium conditions. The interface models are validated against tension and shear tests on bi-block prisms from the literature. Applications to numerical and experimental out-of-plane loaded masonry walls as well as to circular arches with mortar joints are presented to evaluate the effects of tensile strength and the accuracy of the developed model against responses involving P-Δ effects. Comparisons with experimental tests on shear walls also involving cracking of the units in the failure mechanisms are finally reported to discuss the potentialities and limitations of the proposed modeling approach.