{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T12:26:02Z","timestamp":1771935962638,"version":"3.50.1"},"reference-count":49,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,4,25]],"date-time":"2023-04-25T00:00:00Z","timestamp":1682380800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"LAETA","award":["UIDB\/50022\/2020"],"award-info":[{"award-number":["UIDB\/50022\/2020"]}]},{"name":"LAETA","award":["SFRH\/BD\/151362\/2021"],"award-info":[{"award-number":["SFRH\/BD\/151362\/2021"]}]},{"name":"Portuguese Foundation for Science and Technology (FCT)","award":["UIDB\/50022\/2020"],"award-info":[{"award-number":["UIDB\/50022\/2020"]}]},{"name":"Portuguese Foundation for Science and Technology (FCT)","award":["SFRH\/BD\/151362\/2021"],"award-info":[{"award-number":["SFRH\/BD\/151362\/2021"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bioengineering"],"abstract":"<jats:p>Multiscale techniques, namely homogenization, result in significant computational time savings in the analysis of complex structures such as lattice structures, as in many cases it is inefficient to model a periodic structure in full detail in its entire domain. The elastic and plastic properties of two TPMS-based cellular structures, the gyroid, and the primitive surface are studied in this work through numerical homogenization. The study enabled the development of material laws for the homogenized Young\u2019s modulus and homogenized yield stress, which correlated well with experimental data from the literature. It is possible to use the developed material laws to run optimization analyses and develop optimized functionally graded structures for structural applications or reduced stress shielding in bio-applications. Thus, this work presents a study case of a functionally graded optimized femoral stem where it was shown that the porous femoral stem built with Ti-6Al-4V can minimize stress shielding while maintaining the necessary load-bearing capacity. It was shown that the stiffness of cementless femoral stem implant with a graded gyroid foam presents stiffness that is comparable to that of trabecular bone. Moreover, the maximum stress in the implant is lower than the maximum stress in trabecular bone.<\/jats:p>","DOI":"10.3390\/bioengineering10050515","type":"journal-article","created":{"date-parts":[[2023,4,26]],"date-time":"2023-04-26T01:44:42Z","timestamp":1682473482000},"page":"515","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Multiscale Homogenization Techniques for TPMS Foam Material for Biomedical Structural Applications"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3462-2102","authenticated-orcid":false,"given":"Ana","family":"Pais","sequence":"first","affiliation":[{"name":"INEGI\u2014Institute of Science and Innovation in Mechanical and Industrial Engineering, Rua Dr. Roberto Frias, s\/n, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9327-9092","authenticated-orcid":false,"given":"Jorge Lino","family":"Alves","sequence":"additional","affiliation":[{"name":"INEGI\u2014Institute of Science and Innovation in Mechanical and Industrial Engineering, Rua Dr. Roberto Frias, s\/n, 4200-465 Porto, Portugal"},{"name":"FEUP\u2014Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, s\/n, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7281-579X","authenticated-orcid":false,"given":"Renato Natal","family":"Jorge","sequence":"additional","affiliation":[{"name":"INEGI\u2014Institute of Science and Innovation in Mechanical and Industrial Engineering, Rua Dr. Roberto Frias, s\/n, 4200-465 Porto, Portugal"},{"name":"FEUP\u2014Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, s\/n, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0539-7057","authenticated-orcid":false,"given":"Jorge","family":"Belinha","sequence":"additional","affiliation":[{"name":"INEGI\u2014Institute of Science and Innovation in Mechanical and Industrial Engineering, Rua Dr. Roberto Frias, s\/n, 4200-465 Porto, Portugal"},{"name":"ISEP\u2014School of Engineering, Polytechnic of Porto, Rua Dr. Ant\u00f3nio Bernardino de Almeida, 431, 4249-015 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,25]]},"reference":[{"key":"ref_1","unstructured":"Wolff, J. 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