A Voronoi-Diagram-Based Load Transfer Rule: An Application to Damage Evolution in Suddenly Loaded Arrays of Pillars

Arrays of pillars fabricated on flat substrates belong to a class of multicomponent systems composed of many interconnected elements functioning in parallel. Under sudden loading, their load-bearing capacity depends not only on the intrinsic strength of individual pillars but also on the mechanism by which loads released from crushed pillars are redistributed to surviving ones. Following the initial application of load, pillars with thresholds below the applied stress collapse, and their loads are transferred according to a prescribed load-sharing rule, triggering bursts of failures. These bursts may either drive the system to complete collapse or stabilise it in a partially damaged configuration. In this work, we introduce a novel phenomenological load transfer rule that explicitly incorporates the system geometry and the elastic properties of the substrate. When the pillars are placed on a homogeneous, isotropic substrate and crushing occurs instantaneously, the redistributed loads are transferred to intact pillars located within the Voronoi cells defined by the ones failed simultaneously. Since the locations of crushed pillars evolve during the loading process, the Voronoi load sharing (VLS) rule is inherently dynamic rather than static. Within the fibre bundle model framework, we simulate suddenly loaded pillar arrays to evaluate their overall strength and to characterise the spatio-temporal evolution of damage under the VLS rule. These findings are systematically compared with those obtained from other established load-transfer rules.