[{"status":"public","abstract":[{"text":"Rubber-metal bushings (RMB) are critical components in multi-body systems, such as vehicles and industrial machinery, due to their ability to enable relative motion, dampen vibrations, and transmit forces. However, their nonlinear behavior challenges accurate modeling. Traditional physics-based models often fail to balance simplicity, accuracy, and computational efficiency. The growing availability of experimental data offers opportunities to improve RMB modeling through hybrid and data-driven approaches. This study evaluates physics-based, hybrid, and data-driven methods based on predictive accuracy, modeling effort, and computational cost. Hybrid approaches, combining machine learning techniques with physics-based models, are investigated to leverage their complementary strengths. Results show that hybrid methods enhance accuracy for simpler models with a modest increase in computational time. This highlights their potential to simplify RMB modeling while balancing accuracy and efficiency, offering insights for advancing multi-body system simulations. Building on these insights, data-driven methods are explored for their ability to provide surrogate models for dynamical systems without requiring expert knowledge. Experiments reveal that while simple data-driven methods approximate system behavior when data has low variance, they fail with trajectories of widely varying frequency and amplitude.","lang":"eng"}],"publication":"Multibody System Dynamics","type":"journal_article","language":[{"iso":"eng"}],"department":[{"_id":"151"}],"user_id":"43991","_id":"63765","page":"1–21","citation":{"bibtex":"@article{Wohlleben_Schütte_Berkemeier_Sextro_Peitz_2026, title={Evaluating Physics-Based, Hybrid, and Data-Driven Models for Rubber-Metal Bushings}, DOI={<a href=\"https://doi.org/10.1007/s11044-026-10146-9\">10.1007/s11044-026-10146-9</a>}, journal={Multibody System Dynamics}, author={Wohlleben, Meike Claudia and Schütte, Jan and Berkemeier, Manuel Bastian and Sextro, Walter and Peitz, Sebastian}, year={2026}, pages={1–21} }","mla":"Wohlleben, Meike Claudia, et al. “Evaluating Physics-Based, Hybrid, and Data-Driven Models for Rubber-Metal Bushings.” <i>Multibody System Dynamics</i>, 2026, pp. 1–21, doi:<a href=\"https://doi.org/10.1007/s11044-026-10146-9\">10.1007/s11044-026-10146-9</a>.","short":"M.C. Wohlleben, J. Schütte, M.B. Berkemeier, W. Sextro, S. Peitz, Multibody System Dynamics (2026) 1–21.","apa":"Wohlleben, M. C., Schütte, J., Berkemeier, M. B., Sextro, W., &#38; Peitz, S. (2026). Evaluating Physics-Based, Hybrid, and Data-Driven Models for Rubber-Metal Bushings. <i>Multibody System Dynamics</i>, 1–21. <a href=\"https://doi.org/10.1007/s11044-026-10146-9\">https://doi.org/10.1007/s11044-026-10146-9</a>","ama":"Wohlleben MC, Schütte J, Berkemeier MB, Sextro W, Peitz S. Evaluating Physics-Based, Hybrid, and Data-Driven Models for Rubber-Metal Bushings. <i>Multibody System Dynamics</i>. Published online 2026:1–21. doi:<a href=\"https://doi.org/10.1007/s11044-026-10146-9\">10.1007/s11044-026-10146-9</a>","chicago":"Wohlleben, Meike Claudia, Jan Schütte, Manuel Bastian Berkemeier, Walter Sextro, and Sebastian Peitz. “Evaluating Physics-Based, Hybrid, and Data-Driven Models for Rubber-Metal Bushings.” <i>Multibody System Dynamics</i>, 2026, 1–21. <a href=\"https://doi.org/10.1007/s11044-026-10146-9\">https://doi.org/10.1007/s11044-026-10146-9</a>.","ieee":"M. C. Wohlleben, J. Schütte, M. B. Berkemeier, W. Sextro, and S. Peitz, “Evaluating Physics-Based, Hybrid, and Data-Driven Models for Rubber-Metal Bushings,” <i>Multibody System Dynamics</i>, pp. 1–21, 2026, doi: <a href=\"https://doi.org/10.1007/s11044-026-10146-9\">10.1007/s11044-026-10146-9</a>."},"year":"2026","publication_identifier":{"issn":["1384-5640"]},"quality_controlled":"1","doi":"10.1007/s11044-026-10146-9","title":"Evaluating Physics-Based, Hybrid, and Data-Driven Models for Rubber-Metal Bushings","date_created":"2026-01-27T15:51:55Z","author":[{"first_name":"Meike Claudia","last_name":"Wohlleben","orcid":"0009-0009-9767-7168","full_name":"Wohlleben, Meike Claudia","id":"43991"},{"first_name":"Jan","full_name":"Schütte, Jan","id":"22109","last_name":"Schütte","orcid":"0000-0001-9025-9742"},{"full_name":"Berkemeier, Manuel Bastian","last_name":"Berkemeier","first_name":"Manuel Bastian"},{"first_name":"Walter","id":"21220","full_name":"Sextro, Walter","last_name":"Sextro"},{"last_name":"Peitz","full_name":"Peitz, Sebastian","first_name":"Sebastian"}],"date_updated":"2026-03-03T06:31:03Z"},{"year":"2026","citation":{"short":"M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, R.T. Sato Martín de Almagro, Multibody System Dynamics (2026).","mla":"Konopik, Michael, et al. “On the Variational Discretisation of Optimal Control Problems for Unconstrained Lagrangian Dynamics.” <i>Multibody System Dynamics</i>, Springer Science and Business Media LLC, 2026, doi:<a href=\"https://doi.org/10.1007/s11044-025-10138-1\">10.1007/s11044-025-10138-1</a>.","bibtex":"@article{Konopik_Leyendecker_Maslovskaya_Ober-Blöbaum_Sato Martín de Almagro_2026, title={On the variational discretisation of optimal control problems for unconstrained Lagrangian dynamics}, DOI={<a href=\"https://doi.org/10.1007/s11044-025-10138-1\">10.1007/s11044-025-10138-1</a>}, journal={Multibody System Dynamics}, publisher={Springer Science and Business Media LLC}, author={Konopik, Michael and Leyendecker, Sigrid and Maslovskaya, Sofya and Ober-Blöbaum, Sina and Sato Martín de Almagro, Rodrigo T.}, year={2026} }","apa":"Konopik, M., Leyendecker, S., Maslovskaya, S., Ober-Blöbaum, S., &#38; Sato Martín de Almagro, R. T. (2026). On the variational discretisation of optimal control problems for unconstrained Lagrangian dynamics. <i>Multibody System Dynamics</i>. <a href=\"https://doi.org/10.1007/s11044-025-10138-1\">https://doi.org/10.1007/s11044-025-10138-1</a>","ama":"Konopik M, Leyendecker S, Maslovskaya S, Ober-Blöbaum S, Sato Martín de Almagro RT. On the variational discretisation of optimal control problems for unconstrained Lagrangian dynamics. <i>Multibody System Dynamics</i>. Published online 2026. doi:<a href=\"https://doi.org/10.1007/s11044-025-10138-1\">10.1007/s11044-025-10138-1</a>","chicago":"Konopik, Michael, Sigrid Leyendecker, Sofya Maslovskaya, Sina Ober-Blöbaum, and Rodrigo T. Sato Martín de Almagro. “On the Variational Discretisation of Optimal Control Problems for Unconstrained Lagrangian Dynamics.” <i>Multibody System Dynamics</i>, 2026. <a href=\"https://doi.org/10.1007/s11044-025-10138-1\">https://doi.org/10.1007/s11044-025-10138-1</a>.","ieee":"M. Konopik, S. Leyendecker, S. Maslovskaya, S. Ober-Blöbaum, and R. T. Sato Martín de Almagro, “On the variational discretisation of optimal control problems for unconstrained Lagrangian dynamics,” <i>Multibody System Dynamics</i>, 2026, doi: <a href=\"https://doi.org/10.1007/s11044-025-10138-1\">10.1007/s11044-025-10138-1</a>."},"publication_status":"published","publication_identifier":{"issn":["1384-5640","1573-272X"]},"title":"On the variational discretisation of optimal control problems for unconstrained Lagrangian dynamics","doi":"10.1007/s11044-025-10138-1","publisher":"Springer Science and Business Media LLC","date_updated":"2026-01-12T11:35:27Z","author":[{"last_name":"Konopik","full_name":"Konopik, Michael","first_name":"Michael"},{"first_name":"Sigrid","full_name":"Leyendecker, Sigrid","last_name":"Leyendecker"},{"id":"87909","full_name":"Maslovskaya, Sofya","last_name":"Maslovskaya","first_name":"Sofya"},{"first_name":"Sina","last_name":"Ober-Blöbaum","id":"16494","full_name":"Ober-Blöbaum, Sina"},{"last_name":"Sato Martín de Almagro","full_name":"Sato Martín de Almagro, Rodrigo T.","first_name":"Rodrigo T."}],"date_created":"2026-01-12T11:33:54Z","abstract":[{"lang":"eng","text":"We discretise a recently proposed new Lagrangian approach to optimal control problems with dynamics described by force-controlled Euler-Lagrange equations (Konopik et al., in Nonlinearity 38:11, 2025). The resulting discretisations are in the form of discrete Lagrangians. We show that the discrete necessary conditions for optimality obtained provide variational integrators for the continuous problem, akin to Karush-Kuhn-Tucker (KKT) conditions for standard direct approaches. This approach paves the way for the use of variational error analysis to derive the order of convergence of the resulting numerical schemes for both state and costate variables and to apply discrete Noether’s theorem to compute conserved quantities, distinguishing itself from existing geometric approaches. We show for a family of low-order discretisations that the resulting numerical schemes are ‘doubly-symplectic’, meaning they yield forced symplectic integrators for the underlying controlled mechanical system and overall symplectic integrators in the state-adjoint space. Multi-body dynamics examples are solved numerically using the new approach. In addition, the new approach is compared to standard direct approaches in terms of computational performance and error convergence. The results highlight the advantages of the new approach, namely, better performance and convergence behaviour of state and costate variables consistent with variational error analysis and automatic preservation of certain first integrals."}],"status":"public","type":"journal_article","publication":"Multibody System Dynamics","language":[{"iso":"eng"}],"_id":"63557","user_id":"87909","department":[{"_id":"636"}]}]