A multiscale force-based curved beam element for masonry arches

This paper presents a Timoshenko beam finite element for nonlinear analysis of planar masonry arches. Considering small displacement and strain assumption, the element governing equations are defined according to a force-based formulation that adopts three different parametrizations of the axis planar curve, permitting the exact description of the element geometry for arbitrarily curved arches. Specific quadrature techniques are illustrated to perform numerical integration over the curved axis. A two-scale arch-to-beam homogenization procedure reproduces the nonlinear response of periodic masonry materials, where an equivalent Timoshenko straight beam describes the behavior of the reference Unit Cell made of a single linear elastic brick and a nonlinear mortar layer. Formation of the hinges characterizing the collapse mechanism of the arch is detected taking advantage of the quadrature rule along the axis and a fracture energy based regularization technique is employed to avoid damage localization. The proposed curved beam model is implemented in a standard FE analysis code and is used to perform several numerical applications. After validating the proposed formulation through benchmarking tests under linear elastic material response, the numerical simulation of six experimental tests is shown, concerning masonry arches characterized by different shapes and undergoing in-plane bending. The numerical results are validated through experimental outcomes and other FE models.