Summary Hybrid simulation reproduces the experimental response of large‐ or even full‐scale structures subjected to a realistic excitation with reduced costs compared with shake table testing. A real‐time control system emulates the interaction between numerical substructures, which replace subparts having well‐established computational models, and physical substructures tested in the laboratory. In this context, state‐space modeling, which is quite popular in the community of automatic control, offers a computationally cheaper alternative to the finite‐element method for implementing nonlinear numerical substructures for fast‐time hybrid simulation, that is, with testing timescale close to one. This standpoint motivated the development of a computational framework based on partitioned time integration, which is well suited for hard real‐time implementations. Partitioned time integration, which relies on a dual assembly of substructures, enables coupling of state‐space equations discretized with heterogeneous time step sizes. In order to avoid actuators stopping at each simulation step, the physical substructure response is integrated with the same rate of control system, whereas a larger time step size is allowed on the numerical substructure compatibly with available computational resources. Fast‐time hybrid simulations of a two‐pier reinforced concrete bridge tested at the EUCENTRE Experimental Laboratory of Pavia, Italy, are presented as verification example.

This article presents a novel approach to model validation and to the calibration of complex structural systems, through the adoption of heterogeneous (numerical/physical) simulation based on dynamic substructuring (HDS). HDS isolates the physical sub-system (PS) that contains the key region of nonlinear behavior of interest and is tested experimentally, separate from the remainder of the system, that is, the numerical subsystem (NS), which is numerically simulated. A parallel partitioned time integrator based on the finite element tearing and interconnecting method plays a central role in solving the coupled system response, enabling a rigorous and stable synchronization between sub-systems and a realistic interaction between PS and numerical sub-system response. This feature enhances the quality of benchmarks for validation and calibration of low-discrepancy models through virtual structural testing. As a proof of concept, we select an old reinforced concrete viaduct, subjected to seismic loading. Several HDS were conducted at the European Laboratory for Structural Assessment in Ispra (Italy) considering two physical piers and related concave sliding bearings as PSs of the heterogeneous system. As a result, the benefit of employing HDS to set benchmarks for model validation and calibration is highlighted, by developing low-discrepancy FE models of critical viaduct components.In order to reduce model discrepancies, more and more often models try to take into account as many of the interacting physical systems as possible and attempt to describe them on scales that can be very refined. As a result, several very different scales -multiscale -need to be identified in which different physics -multiphysics -must be coupled. Along this line, one can observe a growing interest in virtual testing. Its goal is not to replace experimental tests altogether, but to reduce the number of degrees of freedom associated with the physical system by means of the use of appropriate and accurate models. See, among others, Ostergaard et al. [10] for the prediction of an aircraft structural strength or Caignot et al. [11] for the conception of a virtual testing strategy, in order to predict damping of bolted joints employed in the Ariane 5 launcher. However, given the complexity of these problems, difficulties still persist in relation to the solution of both nonlinear models and stochastic problems requiring multiscale and multiphysics methods. In this context, the dynamic substructure coupling method can be very powerful, because it can localize system nonlinearities and allow identification and update of damaged components/sub-systems; thus, when the properties of one or more sub-systems are altered, the modified sub-systems alone need to be re-analyzed while the other substructures remain unaffected and no further analysis is needed [12].Owing to the capabilities of dynamic substructure coupling, heterogeneous (numerical/physical) simulation based on dynamic substructuring (HDS) represents a form of online simulation, which has b...

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