{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T17:43:58Z","timestamp":1779903838163,"version":"3.53.1"},"reference-count":46,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2019,8,17]],"date-time":"2019-08-17T00:00:00Z","timestamp":1566000000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006520","name":"Politechnika Krakowska","doi-asserted-by":"publisher","award":["The APC funded by the Faculty of Mechanical Engineering"],"award-info":[{"award-number":["The APC funded by the Faculty of Mechanical Engineering"]}],"id":[{"id":"10.13039\/501100006520","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>The ankle is one of the most complicated joints in the human body. Its features a plethora of elements with complex behavior. Their functions could be better understood using a planar model of the joint with low parameter count and low numerical complexity. In this study, an accurate planar model of the ankle with optimized material parameters was presented. In order to obtain the model, we proposed an optimizational approach, which fine-tuned the material parameters of two-dimensional links substituting three-dimensional ligaments of the ankle. Furthermore, the cartilage in the model was replaced with Hertzian contact pairs. The model was solved in statics under moment loads up to 5 Nm. The obtained results showed that the structure exhibited angular displacements in the range of the ankle joint and that their range was higher in dorsiflexion than plantarflexion. The structure also displayed a characteristic ramp up of the angular stiffness. The results obtained from the optimized model were in accordance with the experimental results for the ankle. Therefore, the proposed method for fine-tuning the material parameters of its links could be considered viable.<\/jats:p>","DOI":"10.3390\/ma12162621","type":"journal-article","created":{"date-parts":[[2019,8,19]],"date-time":"2019-08-19T06:10:14Z","timestamp":1566195014000},"page":"2621","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["A Planar Model of an Ankle Joint with Optimized Material Parameters and Hertzian Contact Pairs"],"prefix":"10.3390","volume":"12","author":[{"given":"Aleksandra","family":"Borucka","sequence":"first","affiliation":[{"name":"Institute of Applied Mechanics, Cracow University of Technology, 31-155 Cracow, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7816-5193","authenticated-orcid":false,"given":"Adam","family":"Ciszkiewicz","sequence":"additional","affiliation":[{"name":"Institute of Applied Mechanics, Cracow University of Technology, 31-155 Cracow, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,17]]},"reference":[{"key":"ref_1","first-page":"623","article-title":"Methods for designing and fabrication large-size medical models for orthopaedics","volume":"63","author":"Kudasik","year":"2015","journal-title":"Bull. 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