NDLI: Homogenized stiffness matrices for mineralized collagen fibrils and lamellar bone using unit cell finite element models

Content Provider	Springer Nature Link
Author	Vercher, Ana Giner, Eugenio Arango, Camila Tarancón, José E. Fuenmayor, F. Javier
Copyright Year	2013
Abstract	Mineralized collagen fibrils have been usually analyzed like a two-phase composite material where crystals are considered as platelets that constitute the reinforcement phase. Different models have been used to describe the elastic behavior of the material. In this work, it is shown that when Halpin–Tsai equations are applied to estimate elastic constants from typical constituent properties, not all crystal dimensions yield a model that satisfy thermodynamic restrictions. We provide the ranges of platelet dimensions that lead to positive definite stiffness matrices. On the other hand, a finite element model of a mineralized collagen fibril unit cell under periodic boundary conditions is analyzed. By applying six canonical load cases, homogenized stiffness matrices are numerically calculated. Results show a monoclinic behavior of the mineralized collagen fibril. In addition, a 5-layer lamellar structure is also considered where crystals rotate in adjacent layers of a lamella. The stiffness matrix of each layer is calculated applying Lekhnitskii transformations, and a new finite element model under periodic boundary conditions is analyzed to calculate the homogenized 3D anisotropic stiffness matrix of a unit cell of lamellar bone. Results are compared with the rule-of-mixtures showing in general good agreement.
Starting Page	437
Ending Page	449
Page Count	13
File Format	PDF
ISSN	16177959
Journal	Biomechanics and Modeling in Mechanobiology
Volume Number	13
Issue Number	2
e-ISSN	16177940
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2013-06-21
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mineralized collagen fibril Lamellar bone Cortical bone Finite elements Periodic boundary conditions Homogenized stiffness matrix Theoretical and Applied Mechanics Biomedical Engineering Biophysics and Biological Physics
Content Type	Text
Resource Type	Article
Subject	Mechanical Engineering Modeling and Simulation Biotechnology

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