The topological growth method for strain energy stabilization. A general formulation for topology optimization problems based on the physics of bone remodelling

The topological growth method for strain energy stabilization. A general formulation for topology optimization problems based on the physics of bone remodelling | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 25 August 2025 V1 Latest version Share on The topological growth method for strain energy stabilization. A general formulation for topology optimization problems based on the physics of bone remodelling Authors : Amin Alibakhshi , Iñaki Peñaranda Díaz , and Luis Saucedo-Mora 0000-0003-1091-6875 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.175615701.17181416/v1 250 views 137 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract The replacement of mature bone tissue by new bone tissue is a natural and lifelong process known as bone remodeling. This process has similarities with the topological optimization widely use in engineering, as both seek structures that are efficient, lightweight, and strong. And for this reason, bone remodeling-based topology optimization has been a strategy in structural mechanics for finding the optimized layout of mechanical structures. However, bone remodeling-based topology optimization has not been extensively explored, despite its potential benefits, such as simplicity and intuitive formulation, compared to conventional approaches. In this paper, we formulate a topology optimization algorithm based on a strain energy density formulation for bone remodeling. Unlike the original strain energy density-based bone remodeling equation, which is expressed in terms of apparent density, our formulation uses the Young's modulus, as proposed by the updated properties model (UPM) with a mechanics-based approach. We study the performance of the algorithm by demonstrating its application to two-and three-dimensional structures. Mathematically speaking, we observe that the bone remodeling-driven formulation resembles the UPM method under specific parameter settings. Moreover, the bone remodeling formulation produces results comparable to those of conventional topology optimization algorithms. Changing the algorithm's parameter values, the developed optimization formulation can generate both single-material and graded-material optimized structures, offering greater flexibility for various applications. Supplementary Material File (manuscrip_glob_to.pdf) Download 14.08 MB Information & Authors Information Version history V1 Version 1 25 August 2025 Copyright This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License Keywords bone remodeling finite element analysis growth julia programming language topology optimization Authors Affiliations Amin Alibakhshi E.T.S. de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid View all articles by this author Iñaki Peñaranda Díaz E.T.S. de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid View all articles by this author Luis Saucedo-Mora 0000-0003-1091-6875 [email protected] E.T.S. de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid View all articles by this author Metrics & Citations Metrics Article Usage 250 views 137 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Amin Alibakhshi, Iñaki Peñaranda Díaz, Luis Saucedo-Mora. The topological growth method for strain energy stabilization. A general formulation for topology optimization problems based on the physics of bone remodelling. Authorea . 25 August 2025. DOI: https://doi.org/10.22541/au.175615701.17181416/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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