Materials 2022, 15, 5163. https://doi.org/10.3390/ma15155163 www.mdpi.com/journal/materials Article Correlation of Bone Material Model Using Voxel Mesh and Parametric Optimization Kamil Pietroń, Łukasz Mazurkiewicz, Kamil Sybilski * and Jerzy Małachowski Institute of Mechanics and Computational Engineering, Faculty of Mechanical Engineering, Military University of Technology, gen. Sylwestra Kaliskiego 2, 00‐908 Warsaw, Poland; kamil.pietron@wat.edu.pl (K.P.); lukasz.mazurkiewicz@wat.edu.pl (Ł.M.); jerzy.malachowski@wat.edu.pl (J.M.) * Correspondence: kamil.sybilski@wat.edu.pl Abstract: The authors present an algorithm for determining the stiffness of the bone tissue for individual ranges of bone density. The paper begins with the preparation and appropriate mechanical processing of samples from the bovine femur and their imaging using computed tomography and then processing DICOM files in the MIMICS system. During the processing of DICOM files, particular emphasis was placed on defining basic planes along the sides of the samples, which improved the representation of sample geometry in the models. The MIMICS system transformed DICOM images into voxel models from which the whole bone FE model was built in the next step. A single voxel represents the averaged density of the real sample in a very small finite volume. In the numerical model, it is represented by the HEX8 element, which is a cube. All voxels were divided into groups that were assigned average equivalent densities. Then, the previously prepared samples were loaded to failure in a three‐point bending test. The force waveforms as a function of the deflection of samples were obtained, based on which the global stiffness of the entire sample was determined. To determine the stiffness of each averaged voxel density value, the authors used advanced optimization analyses, during which numerical analyses were carried out simultaneously, independently mapping six experimental tests. Ultimately, the use of genetic algorithms made it possible to select a set of stiffness parameters for which the error of mapping the global stiffness for all samples was the smallest. The discrepancies obtained were less than 5%, which the authors considered satisfactory by the authors for such a heterogeneous medium and for samples collected from different parts of the bone. Finally, the determined data were validated for the sample that was not involved in the correlation of material parameters. The stiffness was 7% lower than in the experimental test. Keywords: bone; mechanical properties; material model correlation; optimization; FEA; validation 1. Introduction The aim of the undertaken work was to determine the basic stiffness parameters for various ranges of bone tissue density using the results of experimental studies and optimization based on the genetic algorithm. The proposed methodology of the procedure was tested using a single bovine bone, which was selected due to its structure being similar to human bones, high availability, and large dimensions, which facilitated the preparation of a larger number of samples from just one bone. Most bones in living organisms are supporting structures, with the exception, among others, of teeth and auditory ossicles. Bones are made of bone tissue that is formed during development and growth. They adapt to the transferred loads, so their structures are quite varied. Bone has a hierarchical structure and, from the point of view of the mechanics of a solid, at the macroscopic level, it is a composite material made of two types of bone tissue: compact, termed cortically and spongy–trabecular [1]. In general, it is surrounded by the periosteum, which contains osteoblasts that perform a regenerative and protective Citation: Pietroń, K.; Mazurkiewicz, Ł.; Sybilski, K.; Małachowski, J. Correlation of Bone Material Model Using Voxel Mesh and Parametric Optimization. Materials 2022, 15, 5163. https://doi.org/10.3390/ ma15155163 Academic Editor: Alexey Smolin Received: 30 June 2022 Accepted: 22 July 2022 Published: 25 July 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/license s/by/4.0/).