Discontinuum rocking of rigid masonry macro-blocks using physics engines: analytical, numerical and experimental benchmarking

Rigid block rocking, significant across disciplines from structural to mechanical engineering, remains challenging to predict accurately using continuum-based numerical solutions. Traditional discontinuum simulation methods, although widely employed for modelling particle separation, re-contact, and collision with multiple contact points, often involve prohibitive computational cost. Analytical solutions, while computationally simpler, are limited primarily to straightforward planar cases with regular geometries. Physics engines - simulation platforms initially developed for digital animations and videogames - present an underexplored yet promising alternative for rigorously modelling multi-body rocking mechanics. These engines utilize discontinuum analysis principles comparable to established discrete models like the Distinct Element Method (DEM), but differ notably in contact detection and modelling strategies, typically providing faster, albeit less precise, predictions. This paper explores and enhances the capabilities of two physics engines - Bullet (integrated within Blender) and Vortex (within Vortex Studio) - to numerically simulate free and forced rocking of isolated and stacked rigid blocks, particularly from an earthquake engineering perspective. Rocking during seismic events frequently impacts blocky structural systems, such as unreinforced masonry (URM), posing assessment challenges for complex constructions. Initially, calibrated Bullet and Vortex simulations are compared with results from Housner's analytical equations for free rocking blocks with various aspect ratios. Subsequently, forced rocking responses to sine-pulse and sinusoidal base motions are examined, employing analytical solutions and referencing experimental and DEM-derived data across different frequencies and acceleration amplitudes. Lastly, the study replicates the rocking response of stacked blocks observed in shake-table tests using DEM, Bullet, and Vortex. Comparative analysis demonstrates that calibrated Bullet and Vortex models yield satisfactory accuracy while significantly reducing computational demands compared to conventional DEM approaches. Consequently, physics engines emerge as viable, efficient alternatives for simulating rocking mechanics, relevant both within structural engineering and beyond.