A general method for the determination of the local orthotropic directions of heterogeneous materials : application to bone structures using μCT images

IF 1 Q4 MECHANICS

Mathematics and Mechanics of Complex Systems Pub Date : 2018-10-01 DOI:10.2140/MEMOCS.2018.6.353

C. Cluzel, R. Allena

引用次数: 19

Abstract

To assess the degree (i.e., isotropy, transverse isotropy, or orthotropy) and the directions of anisotropy of a three-dimensional structure, information about its mesostructure is necessary. Usually, a topological analysis of computed tomography or microcomputed tomography images is performed and requires an interpretation of the constitutive elements of the three-dimensional structure, which may lead to a simplistic description of the geometry. In this paper we propose an alternative technique based on a geometric tensor and we use it to analyze 38 representative elementary volumes extracted from 24 specimens of cortical bone in a human femur whose geometries have been reconstructed via microcomputed tomography images.

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一种确定非均质材料局部正交各向异性方向的通用方法:应用于μCT图像的骨结构

为了评估三维结构的各向异性程度(即各向同性、横向各向同性或正交异性)和各向异性方向，有关其介观结构的信息是必要的。通常，对计算机断层扫描或微计算机断层扫描图像进行拓扑分析，需要对三维结构的构成元素进行解释，这可能导致对几何结构的简化描述。在本文中，我们提出了一种基于几何张量的替代技术，并使用它来分析从24个人类股骨皮质骨标本中提取的38个代表性基本体积，这些标本的几何形状已通过微计算机断层扫描图像重建。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematics and Mechanics of Complex Systems MECHANICS-

CiteScore

3.00

自引率

5.30%

发文量

期刊介绍： MEMOCS is a publication of the International Research Center for the Mathematics and Mechanics of Complex Systems. It publishes articles from diverse scientific fields with a specific emphasis on mechanics. Articles must rely on the application or development of rigorous mathematical methods. The journal intends to foster a multidisciplinary approach to knowledge firmly based on mathematical foundations. It will serve as a forum where scientists from different disciplines meet to share a common, rational vision of science and technology. It intends to support and divulge research whose primary goal is to develop mathematical methods and tools for the study of complexity. The journal will also foster and publish original research in related areas of mathematics of proven applicability, such as variational methods, numerical methods, and optimization techniques. Besides their intrinsic interest, such treatments can become heuristic and epistemological tools for further investigations, and provide methods for deriving predictions from postulated theories. Papers focusing on and clarifying aspects of the history of mathematics and science are also welcome. All methodologies and points of view, if rigorously applied, will be considered.