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

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

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dc.contributor.author Vercher Martínez, Ana es_ES
dc.contributor.author Giner Maravilla, Eugenio es_ES
dc.contributor.author Arango Villegas, Camila es_ES
dc.contributor.author Tarancón Caro, José Enrique es_ES
dc.contributor.author Fuenmayor Fernández, Francisco Javier es_ES
dc.date.accessioned 2015-03-10T09:29:30Z
dc.date.available 2015-03-10T09:29:30Z
dc.date.issued 2014-04
dc.identifier.issn 1617-7959
dc.identifier.uri http://hdl.handle.net/10251/47906
dc.description.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 lement 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. es_ES
dc.description.sponsorship The authors acknowledge the Ministerio de Economia y Competitividad the financial support given through the project DPI2010-20990 and the Generalitat Valenciana through the Programme Prometeo 2012/023. The authors thank Ms. Carla Gonzalez Carrillo by her help in the development of some of the numerical models. en_EN
dc.language Inglés es_ES
dc.publisher Springer Verlag (Germany) es_ES
dc.relation.ispartof Biomechanics and Modeling in Mechanobiology es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Mineralized collagen fibril es_ES
dc.subject Lamellar bone es_ES
dc.subject Cortical bone es_ES
dc.subject Finite elements es_ES
dc.subject Periodic boundary conditions es_ES
dc.subject Homogenized stiffness matrix es_ES
dc.subject.classification INGENIERIA MECANICA es_ES
dc.title Homogenized stiffness matrices for mineralized collagen fibrils and lamellar bone using unit cell finite element models es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s10237-013-0507-y
dc.relation.projectID info:eu-repo/grantAgreement/MICINN//DPI2010-20990/ES/APLICACION DEL METODO DE ELEMENTOS FINITOS EXTENDIDO Y MODELOS DE ZONA COHESIVA AL MODELADO MICROESTRUCTURAL DEL DAÑO EN HUESO CORTICAL/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//PROMETEO%2F2012%2F023/ES/MODELADO NUMERICO AVANZADO EN INGENIERIA MECANICA/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Ingeniería Mecánica y de Materiales - Departament d'Enginyeria Mecànica i de Materials es_ES
dc.contributor.affiliation Universitat Politècnica de València. Centro de Investigación en Tecnología de Vehículos - Centre d'Investigació en Tecnologia de Vehicles es_ES
dc.description.bibliographicCitation Vercher Martínez, A.; Giner Maravilla, E.; Arango Villegas, C.; Tarancón Caro, JE.; Fuenmayor Fernández, FJ. (2014). Homogenized stiffness matrices for mineralized collagen fibrils and lamellar bone using unit cell finite element models. Biomechanics and Modeling in Mechanobiology. 13(2):1-21. https://doi.org/10.1007/s10237-013-0507-y es_ES
dc.description.accrualMethod S es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 21 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 13 es_ES
dc.description.issue 2 es_ES
dc.relation.senia 245831
dc.identifier.eissn 1617-7940
dc.contributor.funder Ministerio de Ciencia e Innovación es_ES
dc.contributor.funder Generalitat Valenciana es_ES
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