Explicit Method for the Simulation of the Out-of-Plane Collapse of Unreinforced Masonry Walls: Influence of Hourglass Control, Damping, and Element Formulation

Nonlinear dynamic FEM analyses of unreinforced masonry (URM) must address convergence difficulties in implicit solutions, conditional stability in explicit solutions, and numerical artifacts related to element integration. This study compares implicit and explicit time-integration procedures using a homogenised three-dimensional model of a dry-joint masonry specimen tested on a shake table. The influence of hourglass-control formulation and scale factor, artificial energy, Rayleigh damping coefficient β, linear bulk viscosity, and element formulation was assessed against the experimental displacement response. Before damage initiation, the hourglass-control formulations produced similar responses. After cracking, increasing the scale factor produced a stiffer response and delayed collapse. The selected formulations reproduced the global collapse mechanism with artificial-energy ratios between 5% and 7% during damage propagation and below 10% at collapse. The use of the full value of β or a linear bulk-viscosity parameter of 5.0 reduced the stable time increment by approximately seven times, and the models failed to reproduce the collapse. Under nonlinear conditions, the response was more sensitive to element formulation than to the time-integration procedure. When collapse occurred, the implicit analyses required approximately twice the computational time of the corresponding explicit analyses. The results provide preliminary guidance for explicit FEM simulations of URM.