Simulation of Combined Stresses and Stress Concentration Factor Effects on a Femur Cortical Bones


mechanical properties
stress-strain curve
stress concentration factor
failure criteria simulation

How to Cite

Velez-Cruz, A. J. (2022). Simulation of Combined Stresses and Stress Concentration Factor Effects on a Femur Cortical Bones. Minerva, 3(8), 8-19.


The purposes of this article were to obtain mechanical properties of the dry femur cortical bone samples through a tensile load and stress concentration factor approach and to provide simulations to predict experimental behaviors based on manipulations of certain properties and parameters of the biomaterial. Since bone samples have characteristics and geometries, the development of a mathematical model was necessary to describe the combination of stresses interacting in the bone when a tension load is applied. The samples have average diameters and lengths of 0.5 and 2 inches respectively and were tested using a 10 kN Universal Tensile Machine to determine mechanical properties such as yield and ultimate stress, young module, and fracture, among others. Several simulations were conducted to evaluate failure criteria like “Von Mises”, “Tresca” and “Tsai-Wu”. Finally, was concluded that 83% of the data obtained from the 22 samples observed in the “Stress-Strain” charts showed a directly proportional relationship.


[1] A. Bandyopadhyay and S. Bose, Characterization of Biomaterials, Waltham, MA: Elsevier, 2013.
[2] J. Pelleg, Mechanical Properties of Materials, New York, London: Springer, 2013.
[3] M. Jaffe, W. B. Hammond, P. Tolias and A. Treena, Characterization of Biomaterials, Newark, NJ: Woodhead Publishing, 2012.
[4] G. R. Cointry, R. F. N. A. L. Capozza, E. J. Roldan and J. L. Ferretti, "Biomechanical Background for a Noninvasive Assessment of Bone Strength and Muscle-Bone Interactions," Journal Musculoskeletal Neuron Interact, vol. 4, no. 1, p. 1–11, 2003.
[5] B. Clarke, "Normal Bone Anatomy and Physiology," Clinical Journal of the American Society of Nephrology, vol. 3, no. 3, pp. 131-139, 2008.
[6] M. Basharat, A. Ikhlas and J. Azher, "Study of Mechanical Properties of Bones and Mechanics of Bone Fracture," in Proceedings of 60th Congress of ISTAM, Rajasthan, India, 2015.
[7] W. D. Pilkey, D. F. Pilkey and B. Zhuming, Peterson's Stress Concentration Factors, Hoboken, NJ: John Wiley & Sons, 2020.
[8] E. F. Morgan, G. U. Unnikrisnan and A. I. Hussein, "Bone Mechanical Properties in Healthy and Diseased States," Annu Rev Biomed Eng, vol. 20, no. 1, pp. 119-143, 2018.
[9] A. J. Velez-Cruz, Stress-Strain Diagram, Bayamon, PR: AVC Press, 2022.
[10] D.-3. ASTM Standard, Standard Test Methods for Composite Materials, West Conshohocken, PA: ASTM Press, 2004.
[11] D. Roylance, Stress-Strain Curves, Cambridge, MA: Cambridge MIT Press, 2001.
[12] B. Yang, Stress, Strain and Structural Dynamics, Los Angeles, CA: Academic Press, 2005.
[13] T. L. Anderson, Fracture Mechanics – Fundamentals and Applications, Boca de Raton, FL: CRC Press, 2006.
[14] ASTM Standard, E-8M-01, Standard Test Methods for Tensile Testing of Metallic Materials, West Conshohocken, PA: ASTM Press, 2004.
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