Homogenized Rigid Body and Spring Model (RBSM) for the non-linear dynamic analysis of historic masonry church facades

The present paper presents a series of FE non-linear dynamic analyses performed on masonry church facades subjected to seismic excitation. The facades are modeled as truly 3D structures, because a portion of the perpendicular walls is accounted for. Both pushover and non-linear dynamic analyses are carried out. The structures are discretized using a rigid body and spring model RBSM strategy, having previously homogenized the masonry material. The spring identification is carried out using classic energy equivalence on homogenized stress-strain relationships deduced by an ad-hoc meso-scale holonomic homogenization previously proposed by the authors for in-plane loaded masonries in the static field. The RBSM is implemented into the commercial software Abaqus, where all the discussed analyses are performed. The procedure proved to be robust and efficient and the following advantages are worth mentioning: (1) the homogenized mechanical properties can be directly implemented at structural level with a very limited computational effort, (2) it is not necessary to discretize with refined meshes the elementary cell; (3) the holonomic laws assumed for mortar joints allow for a total displacement formulation of the model, where the only variables entering into the homogenization problem are represented by displacements. On the other hand, it should be finally pointed out that the procedure adopted is intrinsically affected by a certain level of approximation, mainly linked to the simplified hypothesis done to describe the influence that the in-plane behavior has on the out-of-plane homogenized properties. As a matter of fact, the presence of membrane loads (mainly vertical gravity compression) is assumed a priori known for the determination of the out of plane behavior, as well as totally independent from the state of damage and deformation reached during the analyses. As a rule, such a simplification is however considered fully acceptable, allowing to reasonably take into account the increase of both out-of-plane carrying capacity and ultimate ductility.