# Computational Modeling of U-Shaped Seismic Dampers for Structural Damage Mitigation
## 6 Conclusions  
This work advanced the design of U-shaped (USSD) dampers through the development and validation of a computational model for detailed analysis of the local phenomena of stress, strain, and energy dissipation. The key findings are as follows:* Adapting the Richardson method for mesh convergence analysis proves effective for solid mechanics problems, particularly seismic damper modeling. While Richardson extrapolation is frequently used in computational fluid dynamics, this adaptation offers a robust and efficient method to determine reliable mesh densities for accurately simulating seismic damper behavior. * For reliable numerical simulation results of local strain and energy, at least four elements' through-thickness is required in U-shaped dampers. The influence of mesh density on simulation accuracy is less sensitive to maximum local stress than the maximum strain. * Distinct zones of high stress gradients within the damper highlight the coexistence of elastic and localized plastic deformation mechanisms. Elastic regions, primarily contributing to energy storage, and the localized plastic zones responsible for the critical energy dissipation through plastic work demonstrate the potential for damper optimization. * The highest equivalent stresses are at the transitions between flat and curved sections, with local stresses below the ultimate strength confirming adequate nonlinear computation. * The geometry based GS approach proved highly inaccurate for computing the second stiffness compared to the RDS method (primarily due to its focus on geometry), while the RDS method incorporates essential aspects such as material nonlinearity. The proposed computational model demonstrated reliable elastoplastic numerical results for the performance response of U-shaped seismic dampers. This tool should be applied to optimize current designs and to develop new performance-efficient USSDs. The incorporation of a more sophisticated fatigue-damage model should provide the required simulation results for ensuring the damper lifespan and reliability of buildings and structures in seismic regions. Future research should also focus on three key areas: developing simplified, computationally efficient models of U-shaped damper behavior suitable for integration into larger structural analyses; exploring hybrid systems that combine the energy dissipation of U-shaped dampers with the re-centering capabilities of other mechanisms like pre-tensioned tendons or shape memory alloys to mitigate residual deformation; and conducting parametric studies to express the hysteretic behavior of these dampers using key geometric parameters, facilitating the rapid selection process of seismic dampers for diverse applications without complex numerical simulations. A.G.: Investigation, formal analysis, writing--original draft; visualization; data curation; V.T. : conceptualization, methodology, investigation; formal analysis, writing--original draft, writing--review and editing, supervision, project administration; F.B. : writing--review and editing, formal analysis; A.O. : writing--review and editing, formal analysis; J.H. : writing--review and editing, formal analysis; C.G. : software; L.D. : writing--review and editing, supervision; A.-M.H. : writing--review and editing, resources. All authors have read and agreed to the published version of the manuscript. This research was partially funded by the WBI/AGCID RI02 (DIE23-0001) bilateral project between the University of Liege and the Universidad de La Frontera. [PERSON] thanks the Agencia Nacional de Investigacion y Desarrollo (ANID) for the Ph.D. scholarship \"Beca Doctorado Nacional/2020-21200973\". Not applicable. The original contributions presented in the study are included in the article; further inquiries can be directed to the corresponding author. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. * [PERSON] et al.