Iranian Journal of Mechanical Engineering Transactions of ISME

Iranian Journal of Mechanical Engineering Transactions of ISME

Investigation of cortical bone post-yield behavior in nano-indentation test using ALE finite element method

Authors
Babak Saghafi 1
Majid Ghoreishi 1
Keivan Narooei 2
1 Department of Mechanical Engineering, K.N.Toosi University of Technology, Tehran, Iran.
2 Department of Materials Science and Engineering, K.N.Toosi University of Technology, Tehran, Iran.
10.30506/ijmep.2020.117538.1656
Abstract
Nano-indentation test is one of the most common method to study the material post-yielding behavior providing a suitable material model. Nowadays, this test is also used to investigate the pressure-dependent behavior and other mechanical behaviors of bone. Different material models such as Johnson-Cook, von-Mises, Drucker-Prager, and Hill models have been presented to consider the anisotropy, pressure dependency, strain rate, and temperature dependency of cortical bovine bones similar to human bone in tension and compression.
In the present study, using the Arbitrary Eulerian-Lagrangian (ALE) finite element method in Abaqus software with appropriate contact conditions, the material flow and the results of bone pile-up was well predicted with an error of less than 1%. Also, suitable parameters of the extended Drucker-Prager model for predicting post-yielding bovine cortical bone behavior were presented such that the force-displacement curve of test, showed less than 5% deviation from the experimental results. The friction angle 46°, and zero-degree dilation angle along with the frictional contact conditions between the tool and the bone with a coefficient of 0.3 provided the best parameters to predict post-yielding behavior. It was also shown that changing the angle of dilation from zero to 10 degrees can increase the maximum force applied to the bone up to 40%.               
Keywords
Cortical bone
Nano-indentation test
Finite element method
Arbitrary Lagrangian Eulerian method
Extended Drucker-Prager model

Subjects

[1] Tahmasbi, V., and Ghoreishi, M., "Modeling and Multi Objective Optimization of Effective Parameters in Drilling Cortical Bone", Modares Mechanical Engineering, Proceedings of the Advanced Machining and Machine Tools Conference, Vol. 15, pp. 113-119, (2015).
[2] Rho, J.Y., Kuhn-Spearing, L., and Zioupos, P., "Mechanical Properties and the Hierarchical Structure of Bone", Medical Engineering and Physics, Vol. 20, pp. 92-102, (1998).
[3] Li, S., Abdel-Wahab, A., Demirci, E., and Silberschmidt, V. V, "Penetration of Cutting Tool into Cortical Bone: Experimental and Numerical Investigation of Anisotropic Mechanical Behaviour", Journal of Biomechanics, Vol. 47, pp. 1117-1126, (2014).
[4] Rho, J.Y., "An Ultrasonic Method for Measuring the Elastic Properties of Human Tibial Cortical and Cancellous Bone", Ultrasonics, Vol. 34, pp. 777-783, (1996).
[5] Reilly, D.T., and Burstein, A.H., "The Elastic and Ultimate Properties of Compact Bone Tissue", Journal of Biomechanics, Vol. 8, pp. 393-405, (1975).
[6] Yamada, H., and Evans, F.G., "Strength of Biological Materials", Baltimore, MD, (1970).
[7] Alam, K., Mitrofanov, A.V., and Silberschmidt, V. V., "Thermal Analysis of Orthogonal Cutting of Cortical Bone using Finite Element Simulations", International Journal of Experimental and Computational Biomechanics, Vol. 1, No. 3, pp. 236-251, (2010).
[8] Santiuste, C., Rodríguez-Millán, M., Giner, E., and Miguélez, H., "The Influence of Anisotropy In Numerical Modeling of Orthogonal Cutting of Cortical Bone", Composite Structures, Vol. 116, pp. 423-431, (2014).
[9] Mercer, C., He, M.Y., Wang, R., and Evans, A.G., "Mechanisms Governing the Inelastic Deformation of Cortical Bone and Application to Trabecular Bone", Acta Biomaterialia, Vol. 2, pp. 59-68, (2006).
[10] Novitskaya, E., Chen, P.Y., Lee, S., Castro-Ceseña, A., Hirata, G., Lubarda, V.A., and Mckittrick, J., "Anisotropy in the Compressive Mechanical Properties of Bovine Cortical Bone and the Mineral and Protein Constituents", Acta Biomaterialia, Vol. 7, pp. 3170- 3177, (2011).
[11] Manilay, Z., Novitskaya, E., Sadovnikov, E., and Mckittrick, J., "A Comparative Study of Young and Mature Bovine Cortical Bone", Acta Biomaterialia, Vol. 9, pp. 5280-5288, (2013).
[12] Tai, K., Ulm, F. J., and Ortiz, C., "Nanogranular Origins of the Strength of Bone", Nano Letters, Vol. 6, pp. 2520-2525, (2006).
[13] Mullins, L.P., Bruzzi, M.S., and Mchugh, P.E., "Calibration of a Constitutive Model for the Post-yield Behaviour of Cortical Bone", Journal of the Mechanical Behavior of Biomedical Materials, Vol. 2, pp. 460-470, (2009).
[14] Farrissey, L.M., and Mchugh, P.E., "Determination of Elastic and Plastic Material Properties using Indentation: Development of Method and Application to a Thin Surface Coating", Materials Science and Engineering A, Vol. 399, pp. 254-266, (2005).
[15] Movahhedy, M., Gadala, M.S., and Altintas, Y., "Simulation of the Orthogonal Metal Cutting Process using an Arbitrary Lagrangian-Eulerian Finite-element Method", Journal of Materials Processing Technology, Vol. 103, pp. 267-275, (2000).
[16] Donea, J., Huerta, A., J. Ph., P., and Rodríguez-Ferrán, A., "Arbitrary Lagrangian-Eulerian Methods, Encyclopedia of Computational Mechanics", Vol. 1, Fundamentals. John Wiley & Sons, Ltd. ISBN: 0-470-84699-2. (2004).
[17] Pantalé, O., Rakotomalala, R., and Touratier, M., "An Ale Three-dimensional Model of Orthogonal and Oblique Metal Cutting Processes", International Journal of Forming Processes, Vol. 1. pp. 371-388, (1998).
[18] Saghafi, B., Ghoreishi, M., and Narooei, K., "Prediction of Safe Zone for Osteonecrosis in the Cutting Process of Bovine Cortical Femur Bone using Arbitrary Lagrangian-Eulerian Method and Multi-objective Optimization", International Journal of Advanced Manufacturing Technology, Vol. 104, pp. 2031-2043, (2019).
[19] Demiral, M., Abdel-Wahab, A., and Silberschmidt, V., "A Numerical Study on Indentation Properties of Cortical Bone Tissue: Influence of Anisotropy", Acta of Bioengineering and Biomechanics, Vol. 17, pp. 3-14, (2015).
[20] Oliver, W.C., and Pharr, G.M., "Measurement of Hardness and Elastic Modulus by Instrumented Indentation: Advances in Understanding and Refinements to Methodology", Journal of Materials Research, Vol. 19, pp. 3-20, (2004).
[21] Oliver, W.C., and Pharr, G.M., "An Improved Technique for Determining Hardness and Elastic Modulus using Load and Displacement Sensing Indentation Experiments", Journal of Materials Research, Vol. 7, pp. 1564-1583, (1992).
[22] Drucker, D.C., and Prager, W., "Soil Mechanics and Plastic Analysis or Limit Design", Quarterly of Applied Mathematics, Vol. 10, pp. 157-165, (1952).
[23] Mijangos, I., and Kelly, K.U.O., "Drucker-Prager Finite Element Constitutive Model of Microindentation in Polycrystalline Alumina", Sem Annual Conference & Exposition on Experimental & Applied Mechanics Proceedings, Vol. 4, pp. 2704-2712, Albuquerque, New Mexico, USA, (2009).
[24] Toal, V.R., "The Mechanics of Microdamage\Rand Microfracture in Trabecular Bone", Doctoral Dissertation, Queensland University of Technology, Australia, (2013).
[25] Adam, C.J., and Swain, M. V., "The Effect of Friction on Indenter Force and Pile-up in Numerical Simulations of Bone Nanoindentation", Journal of the Mechanical Behavior of Biomedical Materials, Vol. 4, pp. 1554-1558, (2011).
[26] Carnelli, D., Lucchini, R., Ponzoni, M., Contro, R., and Vena, P., "Nanoindentation Testing and Finite Element Simulations of Cortical Bone Allowing for Anisotropic Elastic and Inelastic Mechanical Response", Journal of Biomechanics, Vol. 44, pp. 1852-1858, (2011).

  • Receive Date 25 November 2019
  • Revise Date 23 April 2020
  • Accept Date 11 November 2020