Constitutive modelling of inelastic behaviour of cortical bone

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Natali, Arturo N.¹; Carniel, Emanuele L.¹; Pavan, Piero G.¹

Constitutive modelling of inelastic behaviour of cortical bone

Med Eng Phys. September 2008;30(7):905-912

Affiliations

¹University of Padova, Centre of Mechanics of Biological Materials, Via F. Marzolo 9, I-3531 Padova, Italy
Abstract and keywords

A visco-elasto-plastic constitutive model is formulated for investigating the mechanics of cortical bone tissue, accounting for an anisotropic configuration and post-elastic and time-dependent phenomena. The constitutive model is developed with reference to experimental data obtained from literature on the behaviour of cortical bone taken from multiple samples. Regarding the constitutive model, a specific procedure based on a coupled deterministic and stochastic method is applied in order to determine the values of the constitutive parameters with regard to human samples. The procedure entails processing of data deduced from mechanical tests to achieve relationships between permanent and total strain, elastic modulus and strain rate, and creep elastic modulus and time. Numerical results obtained by using a finite element model are compared with tensile experimental data on cortical bone including the post-elastic range and creep phenomena. The model shows an excellent capability to describe the tensile behaviour of the cortical bone for the specific mechanical condition analysed.

Keywords: Bone tissue; Constitutive model; Plasticity; Visco-elasticity
Links

DOI: 10.1016/j.medengphy.2007.12.001

PubMed: 18207444

WoS: 000259768300013
History

Received: 2007-07-17

Revised: 2007-11-29

Accepted: 2007-12-2

Online: 2008-01-22

Cited Works (14)

Year	Entry
2004	Iyo T, Maki Y, Sasaki N, Nakata M. Anisotropic viscoelastic properties of cortical bone. J Biomech. September 2004;37(9):1433-1437.
1974	Crowninshield RD, Pope MH. The response of compact bone in tension at various strain rates. Ann Biomed Eng. 1974;2(2):217-225.
2006	Akhtar R, Eichhorn SJ, Mummer PM. Microstructure-based finite element modelling and characterisation of bovine trabecular bone. J Bionic Eng. 2006;3(1):3-9.
2007	Fritsch A, Hellmich C. “Universal” microstructural patterns in bone: micromechanics-based prediction of anisotropic material behavior. J Theo Biol. February 21, 2007;244(4):597-620.
2004	Dong XN, Guo XE. The dependence of transversely isotropic elasticity of human femoral cortical bone on porosity. J Biomech. August 2004;37(8):1281-1287.
2006	Mercer C, He MY, Wang R, Evans AG. Mechanisms governing the inelastic deformation of cortical bone and application to trabecular bone. Acta Biomater. January 2006;2(1):59-68.
2004	Currey JD. Tensile yield in compact bone is determined by strain, post-yield behaviour by mineral content. J Biomech. April 2004;37(4):549-556.
2003	Stölken JS, Kinney JH. On the importance of geometric nonlinearity in finite-element simulations of trabecular bone failure. Bone. October 2003;33(4):494-504.
1999	Chang WCW, Christensen TM, Pinilla TP, Keaveny TM. Uniaxial yield strains for bovine trabecular bone are isotropic and asymmetric. J Orthop Res. July 1999;17(4):582-585.
2006	van Lenthe GH, Stauber M, Müller R. Specimen-specific beam models for fast and accurate prediction of human trabecular bone mechanical properties. Bone. December 2006;39(6):1182-1189.
2004	Bayraktar HH, Morgan EF, Niebur GL, Morris GE, Wong EK, Keaveny TM. Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue. J Biomech. January 2004;37(1):27-35.
2001	Cowin SC, ed. Bone Mechanics Handbook. 2nd ed. Boca Raton, FL: CRC Press; 2001.
2001	Keaveny TM, Morgan EF, Niebur GL, Yeh OC. Biomechanics of trabecular bone. Annu Rev Biomed Eng. 2001;3:307-333.
1989	Cowin SC, Mehrabadi MM. Identification of the elastic symmetry of bone and other materials. J Biomech. 1989;22(6-7):503-515.

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2019	Marques M, Belinha J, Oliveira AF, Manzanares-Céspedes MC, Jorge RN. Combining radial point interpolation meshless method with a new homogenization technique for trabecular bone multiscale structural analyses. Acta Bioeng Biomech. 2019;21(2):101-113.
2010	Charlebois M, Jirásek M, Zysset PK. A nonlocal constitutive model for trabecular bone softening in compression. Biomech Model Mechanobiol. 2010;9(5):597-611.
2013	Hambli R. Micro-CT finite element model and experimental validation of trabecular bone damage and fracture. Bone. October 2013;56(2):363-374.
2020	Kraiem T, Barkaoui A, Merzouki T, Chafra M. Computational approach of the cortical bone mechanical behavior based on an elastic viscoplastic damageable constitutive model. Int J Appl Mech. 2020;2(7):2050081.
2012	Kelly N, McGarry JP. Experimental and numerical characterisation of the elasto-plastic properties of bovine trabecular bone and a trabecular bone analogue. J Mech Behav Biomed Mater. May 2012;9:184-197.
2013	Ridha H, Thurner PJ. Finite element prediction with experimental validation of damage distribution in single trabeculae during three-point bending tests. J Mech Behav Biomed Mater. November 2013;27:94-106.
2020	Lovrenić-Jugović M, Tonković Z, Skozrit I. Experimental and numerical investigation of cyclic creep and recovery behavior of bovine cortical bone. Mech Mater. July 2020;146:103407.
2010	Natali AN, Fontanella CG, Carniel EL. Constitutive formulation and analysis of heel pad tissues mechanics. Med Eng Phys. 2010;32(5):516-522.
2014	Carretta R. Post-Yield Mechanics and Material Composition of Single Trabeculae: A Combined Experimental and Modelling Approach [PhD thesis]. Swiss Federal Institute of Technology Zürich; 2014.
2012	Deymier-Black AC. Study of the Elasto-Plastic Properties of Mineralized Biomaterials Via Synchrotron High-Energy X-Ray Diffraction [PhD thesis]. Evanston, IL: Northwestern University; June 2012.
2012	Yuan F. Finite Element Simulation of the Mechanical Properties of Mineralized Biomaterials [PhD thesis]. Evanston, IL: Northwestern University; August 2012.
2012	Zhao Y. Bone Indentation Modeling Via Analytical and Finite Element Methods [PhD thesis]. University of Notre Dame; March 2012.
2012	Kelly N. An Experimental and Computational Investigation of the Inelastic Behaviour of Trabecular Bone [PhD thesis]. Galway, Ireland: National University of Ireland Galway; September 2012.
2018	Zimmermann Y. Développement d'une modélisation par éléments finis pour caractérisation non destructive de la biomécanique osseuse à partir d'images MICRO-CT [Master's thesis]. École polytechnique de Montréal; December 2018.
2009	Lievers WB. Effects of Geometric and Material Property Changes on the Apparent Elastic Properties of Cancellous Bone [PhD thesis]. Queen's University; April 2009.
2021	Frank M. Mechanical Characterization of Individual Trabeculae [PhD thesis]. Vienna University of Technology; February 2021.
2014	Schwiedrzik JJ. Experimental, Theoretical and Numerical Investigation of the Nonlinear Micromechanical Properties of Bone [PhD thesis]. Universität Bern; 2014.
2020	Hamandi FMRA. Hierarchical Structure, Properties and Bone Mechanics At Macro, Micro, and Nano Levels [PhD thesis]. Dayton, OH: Wright State University; 2020.