Rigid block analysis of masonry structures with geometrical and material nonlinearity

Structural modeling of masonry constructions is a critical area of research, essential for preserving the architectural heritage worldwide, and for the structural safety of a high number of contemporary buildings. Rigid block models prove to be an effective approach, especially for historic masonry constructions. They can effectively represent the effects of the high compressive strength and the low deformability of the blocks in comparison to the low strength and stiffness of joints. The nonlinear response of masonry structures substantially depends on the behavior of the interfaces due to unilateral contact and frictional effects. Moreover, the evolution of mechanisms in masonry structures involves finite rotations, and therefore large displacements, a further source of structural nonlinearity. Neglecting large displacements by approximating the deformed configuration by the undeformed one might lead to non-negligible errors. The above modeling choices are adopted in the distinct element method, also implemented in some well-known commercial software. However, these codes are not specifically conceived for masonry structures but for simulating the mechanical behavior of granular materials such as soil, rocks, and powders. This motivates ongoing research on the development of rigid block models directly aimed at the structural assessment. In this context, a masonry rigid block model is proposed, based on a careful determination of the tangent stiffness interface matrix in presence of geometrical and material nonlinearity. This innovative approach can be approximated and simplified in the case of moderate rotations in large displacements. In particular, a consistent formulation for a 2D interface model in large displacements is established by introducing a co-rotational reference system coincident with the middle-line between the two deformed sides of the interface shared by two rigid blocks. A numerical procedure, based on the backward Euler time-integration scheme, is introduced, and the time step is solved adopting a displacement driven predictor-corrector algorithm. For the solution, the classical iterative Newton-Raphson scheme is adopted by linearizing nonlinear terms. The model is discussed through numerical simulations on different masonry structures, conducted in both displacement control and arc-length control scenarios. The results include a comparison of solutions obtained with finite rotation and moderate rotation theories.