A Novel Non-Linear Discrete Homogenization Approach for the Analysis of Double Curvature Masonry Structures

In the context of historical heritage, curved masonry structures as arches, vaults and domes represent the most distinctive and charming feature. Since the 17th century, several approaches have been developed in order to analyze their behavior, achieving nowadays techniques enable to combine ancient and modern methods. However, as these elements act as weak points of the structures during seismic events, the necessity of evaluating their vulnerability and safety level pushed the research to implement new numerical approaches. Although, the behavior of such structures is still not deeply investigated in literature as the high number of variables and uncertainty involved. An innovative discrete homogenized model approach is here proposed. The method provides the main features needed for proper simulation of masonry curved structures, including the orthotropy and the typical in-and-out-of-plane coupled behavior exhibited by masonry vaults. Moreover, homogenization procedures directly implemented in the method allows reducing by far the number of variables, leading to non-linear analyses without unpractical computational time. The model is conceived as an assembly of elastic units joint by non-linear interfaces. These latter are modeled as bricks elements and Concrete Damage Plasticity is used for modeling non-linear mechanical properties, coming from homogenization procedures. The discrete mesh is obtained automatically by means of an ad-hoc script. With the aim to validate the proposed approach, some non-linear simulations are carried out on examples of an unreinforced dome, of which experimental and numerical data are available, showing the reliability of the method and the accuracy of reproducing the evolution of the damage with a limited computational burden.