Force-based Finite Element for Modelling the Cyclic Behaviour of Unreinforced Masonry Piers

A performance-based seismic assessment of unreinforced masonry (URM) buildings requires the use of reliable models, able to predict their nonlinear force-displacement response including their displacement capacity. Among the possible methodologies, at different levels of complexity, macro-modelling using structural component elements has proved to be an approach that can provide satisfactory accuracy at very low computational cost, rendering it therefore suitable for engineering practice. The use of such modelling strategy requires the idealization of the structure through an equivalent frame, whose deformable elements are able to describe the in-plane response of piers or spandrels. In this paper, the modelling of the cyclic in-plane response of a modern unreinforced brick masonry panel through a two-node, force-based beam element is proposed and validated against experimental results. The distributed inelasticity is described with the use of numerically integrated fibre sections, applying a nonlinear, biaxial material model. Such model can provide a coupling between axial and shear response at the local level, which is a novel approach for the numerical modelling of URM structural components with beam elements. The model is implemented in the open-source platform “Opensees” and is therefore available to the research community. The validation of the proposed formulation is performed through the comparison with experimental results of a shear and compression test, performed at EPFL. The experimental data, including also strain fields, allow for the comparison with numerical results both at the element level, in terms of top displacement and rotation, and at the local scale, in terms of fibre strains and sectional deformations. The comparison showed that the proposed element captures the cyclic response of unreinforced brick masonry walls in an adequate manner.