A numerical procedure for the force-displacement description of out-of-plane collapse mechanisms in masonry structures

In this paper, a novel numerical procedure is proposed for the force-displacement description of out-of-plane collapse in masonry structures. The numerical procedure herein proposed represents one first attempt to couple limit analysis-based solutions to displacement-based evolutive analysis strategies. Limit-analysis based solutions are considered trustworthy to investigate collapse mechanisms in masonry structures, even though they cannot be used in displacement-based seismic assessment procedures (e.g. pushover analysis), while displacement-based evolutive analysis strategies (e.g. block-based and anisotropic continuum approaches), which can undertake this last task, are typically computationally demanding and their mechanical characterization is often very challenging. In this research, a genetic algorithm NURBS-based adaptive homogenized upper bound limit analysis is firstly adopted to compute the collapse mechanism that the structure (of any geometrical complexity) experiences for a given loading condition. Then, the 3D geometry of the collapse mechanism is imported in incremental-iterative step-by-step evolutive analysis frameworks to perform pushover analysis. In particular, two numerical modelling approaches are conceived to this aim, both lumping all the mechanical nonlinearities into tight zones located in correspondence of the cracks defined in the collapse mechanism previously computed. The first one uses 3D plastic damaging strips governed by a standard nonlinear continuum constitutive law. The second approach adopts non-standard zero-thickness contact-based interfaces governed by a cohesive-frictional contact behaviour previously developed by the authors for the brick-to-brick mechanical interaction. A number of meaningful structural examples show the effectiveness of the numerical procedure proposed. Pushover curves obtained through different modelling strategies are also critically compared.