ABSTRACT The hybrid discrete‐finite element (HybriDFEM) method, previously developed to perform static and modal analysis in discrete and coupled discrete‐finite element models, is extended to nonlinear response‐history analyses. The equations of motion for the HybriDFEM model are solved through various numerical time‐integration schemes, both explicit and implicit, and considering different damping models. Specific examples are presented to assess the effectiveness of the implementation. First, a stability and accuracy analysis is performed on an undamped elastic beam undergoing free vibrations to investigate period elongation with respect to the time step. Next, the dynamic response of a masonry column and masonry arch subjected to impulse loads is evaluated, exploring the performance of HybriDFEM in problems involving rocking, curved geometries, large deformations, and damping. It is shown, by comparison with other discrete element models, that both rocking and full collapse can be captured with fidelity by HybriDFEM, and that implicit schemes can reduce the computational demand with respect to explicit ones without affecting solution accuracy. Although the use of viscous Rayleigh damping defined at the global level is commonly implemented in FEM, key issues related to its use in DEM are raised and explained in this paper, namely the occurrence of mechanisms during the analysis, which can nullify damping forces when tangent stiffness‐proportional damping is employed. In the final example, a response analysis is conducted on a numerical mock‐up representative of a mixed reinforced concrete‐masonry building subjected to ground motion. It demonstrates how complex interactions between structural elements can be captured with realistic simulation timeframes by coupling rigid‐block HybriDFEM representations, for the masonry walls, with standard beam elements, for the reinforced concrete beams and columns.
Bouckaert et al. (2026) studied this question.