# An Overview of Selected Material Properties in Finite Element Modeling of the Human Femur

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Types of Material Properties

#### 1.1.1. Isotropic Materials

#### 1.1.2. Anisotropic Materials

#### 1.1.3. Orthotropic Materials

_{1}, E

_{2}, E

_{3}, G

_{12}, G

_{23}, G

_{31}>0

_{11}, C

_{22}, C

_{33}, C

_{44}, C

_{55}, C

_{66}> 0

_{23}U

_{32}). (1 − U

_{13}U

_{31}). (1 − U

_{12}U

_{21}) > 0

_{12}U

_{21}) − (U

_{23}U

_{32}) − (U

_{31}U

_{13}) − 2(U

_{21}U

_{32}U

_{13}) > 0

#### 1.2. Physical and Mechanical Properties of the Human Femur

^{3}for cortical tissue and 0.4 g/cm

^{3}for trabecular tissue. This is in addition to the mechanical properties indicated.

#### 1.2.1. Material Properties for Trabeculae

- For cancellous bone tissue, the ratios of the directional Young’s moduli exhibit a relationship similar to that reported in [36], where E
_{1}/E_{2}and E_{1}/E_{3}are equal to approximately 2 (here, equal to 1.4 and 2.0, respectively), and E_{3}/E_{2}is equal to approximately 0.6 (here, 0.07). - The typical Young’s modulus is 1.0 GPa, which is in accordance with what has been documented in the literature.

#### 1.2.2. Material Properties for Cortical Bone

_{1}= 8.69 GPa (longitudinal), E

_{2}= 4.19 GPa (transverse), and E

_{3}= 3.76 GPa (radial).

_{1}is substantially lower than that of the majority of other studies: E

_{2}/E

_{1}= 48%, E

_{3}/E

_{2}= 90%, and E

_{3}/E

_{1}= 43%. The longitudinal tensile and bending moduli for wet human cortical bone specimens, principally from the femur, are listed in detail in Table 5 [18]. As can be observed, the average longitudinal Young’s modulus throughout these experiments is 16.0 GPa. Using the aforementioned percentages, E

_{2}and E3 are equivalent to roughly 6.8 GPa and 6.3 GPa, respectively, with E1 equal to 16.0 GPa. Shear moduli are found in Schuster [11] and are comparable to an average shear modulus of 3.36 GPa as reported by Reilly and Burnstein [17]. In another study, Mirzaali et al. [37] evaluated the physical and mechanical properties of cortical bone in different cases. It was written that the axial hardness modulus for osteonal, interstitial, and pooled bone are 408 ± 69, 503 ± 56, and 455 ± 78, respectively. Therefore, transverse hardness moduli for female, male, and pooled bone are 367 ± 91, 428 ± 75, and 395 ± 89 respectively. In uniaxial tests, the moduli are 18.16 ± 1.88 and 18.97 ± 1.84 under uniaxial tension and compression, respectively. The Poisson’s ratios for cortical tissue recorded by Reilly and Burnstein [17] were 0.62 for “radial specimens” and 0.40 for “longitudinal specimens”. Since Poisson ratios greater than 0.5 are not permitted in the infinitesimal theory, these values led to problems in the constitutive equations used for the orthotropic material model. As a result, the ratios were reduced while maintaining their relative magnitudes. The radial and longitudinal Poisson’s ratios are scaled to 0.45 and 0.30, respectively. These are comparable to the average Poisson’s ratio for femoral cortical bone tissue reported by Katsamanis and Raftopoulos [38] of 0.36. The transverse direction of Poisson’s ratio in this study is also calculated using the Poisson’s ratio for the radially harvested specimen (set to 0.3). Table 6 lists the final nine elastic material constants used for the orthotropic cortical bone. The orthotropic material model description with E

_{2}= E

_{3}= 6.30 GPa and G

_{12}= G

_{13}= 3.30 is all that is required to describe the transversely isotropic material model for cortical tissue, as illustrated in Table 7. Table 8 displays the isotropic material model description for cortical tissue. The material constants for the isotropic piecewise linear- plasticity material model of cortical bone are displayed in Table 9. The yield stress is the average of the tension values for specimens tested in by Reilly and Burnstein [17], and the elastic modulus and Poisson’s ratio are the same used for the elastic isotropic model. The tangent modulus is 5% of the elastic modulus [20].

#### 1.2.3. Material Properties for Marrow

## 2. Results

^{2}(based on the mid-diaphysis cross-sectional characteristics of the femur, the proportional limit deflection, and load) and the current investigation reveals a value of 18.0 kN/mm

^{2}that is similar.

^{2}, or less than half of the ultimate torsion strength of 45.3 N/mm

^{2}. The maximum twist angle is roughly 1.5°. According to Cristofolini et al. [16], fresh-frozen femur samples have an elastic stiffness in the torsion range of 6.5–10.5 Nm/deg. The isotropic FE femur model has a higher stiffness of 19.4 Nm/deg, and the orthotropic and transversely isotropic femur models show stiffness in torsion that is closer to the literature at 11.64 Nm/deg. Each FE femur model’s elastic whole bone torsion stiffness is listed in Table 12. The transversely isotropic model and the orthotropic model have identical whole bone elastic torsion stiffnesses, with the isotropic model having a 50% greater stiffness.

## 3. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Bazyar, P.; Baumgart, A. Effects of Additional Mechanisms on The Performance of Workshop Crane. J. Eng. Ind. Res.
**2021**, 3, 87–98. [Google Scholar] [CrossRef] - Bazyar, P.; Jafari, A.; Alimardani, R.; Mohammadi, V.; Grichar, J. Finite Element Analysis of Small-scale Head of Combine Harvester for Harvesting Fine-Grain Products. Int. J. Adv. Biol. Biomed. Res.
**2020**, 8, 340–358. [Google Scholar] [CrossRef] - Jacrot, B. The study of biological structures by neutron scattering from solution. Rep. Prog. Phys.
**1976**, 39, 911–953. [Google Scholar] [CrossRef] - Amini, A.R.; Laurencin, C.T.; Nukavarapu, S.P. Bone Tissue Engineering: Recent Advances and Challenges. Crit. Rev. Biomed. Eng.
**2012**, 40, 363–408. [Google Scholar] [CrossRef][Green Version] - Mather, B.S. Correlations between strength and other properties of long bones. J. Trauma Inj. Infect. Crit. Care
**1967**, 7, 633–638. [Google Scholar] [CrossRef] - Yamada, H.; Evans, F.G. Strength of Biological Materials. 1970. Available online: https://scholar.google.com/scholar?hl=en&as_sdt=0%2C5&q=Yamada%2C+H.%2C+%26+Evans%2C+F.+G.+%281970%29.+Strength+of+biological+materials.&btnG= (accessed on 20 January 2023). [CrossRef]
- Martens, M.; van Audekercke, R.; de Meester, P.; Mulier, J. Mechanical behaviour of femoral bones in bending loading. J. Biomech.
**1986**, 19, 443–454. [Google Scholar] [CrossRef] - Keller, T.S.; Mao, Z.; Spengler, D.M. Young’s modulus, bending strength, and tissue physical properties of human compact bone. J. Orthop. Res.
**1990**, 8, 592–603. [Google Scholar] [CrossRef] - Zani, L.; Erani, P.; Grassi, L.; Taddei, F.; Cristofolini, L. Strain distribution in the proximal Human femur during in vitro simulated sideways fall. J. Biomech.
**2015**, 48, 2130–2143. [Google Scholar] [CrossRef] - Arun, K.V.; Jadhav, K.K. Behaviour of human femur bone under bending and impact loads. Eur. J. Clin. Biomed. Sci.
**2016**, 2, 6–13. [Google Scholar] [CrossRef] - Schuster, P.; Jayaraman, G. Development and validation of a pedestrian lower limb non-linear 3-D finite element model. Stapp Car Crash J.
**2000**, 44, 315. Available online: https://digitalcommons.calpoly.edu/meng_fac/118 (accessed on 20 January 2023). - Pellettiere, J.A. A Dynamic Material Model for Bone. University of Virginia: Charlottesville, VA, USA, 1999; Available online: https://www.proquest.com/openview/4b2efe43d488716177b54e8027c35af6/1?pq-origsite=gscholar&cbl=18750&diss=y (accessed on 20 January 2023).
- Wirtz, D.C.; Schiffers, N.; Pandorf, T.; Radermacher, K.; Weichert, D.; Forst, R. Critical evaluation of known bone material properties to realize anisotropic FE-simulation of the proximal femur. J. Biomech.
**2000**, 33, 1325–1330. [Google Scholar] [CrossRef] - Ciarelli, M.J.; Goldstein, S.A.; Kuhn, J.L.; Cody, D.D.; Brown, M.B. Evaluation of orthogonal mechanical properties and density of human trabecular bone from the major metaphyseal regions with materials testing and computed tomography. J. Orthop. Res.
**1991**, 9, 674–682. [Google Scholar] [CrossRef] - Osterhoff, G.; Morgan, E.F.; Shefelbine, S.J.; Karim, L.; McNamara, L.M.; Augat, P. Bone mechanical properties and changes with osteoporosis. Injury
**2016**, 47, S11–S20. [Google Scholar] [CrossRef][Green Version] - Cristofolini, L.; Viceconti, M.; Cappello, A.; Toni, A. Mechanical validation of whole bone composite femur models. J. Biomech.
**1996**, 29, 525–535. [Google Scholar] [CrossRef] - Reilly, D.T.; Burstein, A.H. The mechanical properties of cortical bone. JBJS
**1974**, 56, 1001–1022. Available online: https://journals.lww.com/jbjsjournal/Citation/1974/56050/The_Mechanical_Properties_of_Cortical_Bone.12.aspx (accessed on 20 January 2023). [CrossRef] - Choi, K.; Kuhn, J.; Ciarelli, M.; Goldstein, S. The elastic moduli of human subchondral, trabecular, and cortical bone tissue and the size-dependency of cortical bone modulus. J. Biomech.
**1990**, 23, 1103–1113. [Google Scholar] [CrossRef][Green Version] - Keaveny, T.M.; Guo, X.; Wachtel, E.F.; McMahon, T.A.; Hayes, W.C. Trabecular bone exhibits fully linear elastic behavior and yields at low strains. J. Biomech.
**1994**, 27, 1127–1136. [Google Scholar] [CrossRef] - Bayraktar, H.H.; Morgan, E.F.; Niebur, G.L.; Morris, G.E.; Wong, E.K.; Keaveny, T.M. Comparison of the elastic and yield properties of human femoral trabecular and cortical bone tissue. J. Biomech.
**2004**, 37, 27–35. [Google Scholar] [CrossRef] - Augat, P.; Link, T.; Lang, T.F.; Lin, J.C.; Majumdar, S.; Genant, H.K. Anisotropy of the elastic modulus of trabecular bone specimens from different anatomical locations. Med. Eng. Phys.
**1998**, 20, 124–131. [Google Scholar] [CrossRef] - Zysset, P.K. A review of morphology–elasticity relationships in human trabecular bone: Theories and experiments. J. Biomech.
**2003**, 36, 1469–1485. [Google Scholar] [CrossRef] - Morgan, E.F.; Bayraktar, H.H.; Keaveny, T.M. Trabecular bone modulus–density relationships depend on anatomic site. J. Biomech.
**2003**, 36, 897–904. [Google Scholar] [CrossRef] - Morgan, E.F.; Keaveny, T.M. Dependence of yield strain of human trabecular bone on anatomic site. J. Biomech.
**2001**, 34, 569–577. [Google Scholar] [CrossRef] - Asgharpour, Z.; Zioupos, P.; Graw, M.; Peldschus, S. Development of a strain rate dependent material model of human cortical bone for computer-aided reconstruction of injury mechanisms. Forensic Sci. Int.
**2014**, 236, 109–116. [Google Scholar] [CrossRef] - Yeni, Y.N.; Brown, C.U.; Wang, Z.; Norman, T.L. The influence of bone morphology on fracture toughness of the human femur and tibia. Bone
**1997**, 21, 453–459. [Google Scholar] [CrossRef] - Falcinelli, C.; Whyne, C. Image-based finite-element modeling of the human femur. Comput. Methods Biomech. Biomed. Eng.
**2020**, 23, 1138–1161. [Google Scholar] [CrossRef] - Chethan, K.N.; Bhat, S.; Zuber, M.; Shenoy, S. Finite Element Analysis of Different Hip Implant Designs along with Femur under Static Loading Conditions. J. Biomed. Phys. Eng.
**2019**, 9, 507–516. [Google Scholar] [CrossRef][Green Version] - Schileo, E.; Pitocchi, J.; Falcinelli, C.; Taddei, F. Cortical bone mapping improves finite element strain prediction accuracy at the proximal femur. Bone
**2020**, 136, 115348. [Google Scholar] [CrossRef] - Zhang, Y.; Li, A.-A.; Liu, J.-M.; Tong, W.-L.; Xiao, S.-N.; Liu, Z.-L. Effect of screw tunnels on proximal femur strength after screw removal: A finite element analysis. Orthop. Traumatol. Surg. Res.
**2022**, 108, 103408. [Google Scholar] [CrossRef] - Kalaiyarasan, A.; Sankar, K.; Sundaram, S. Finite element analysis and modeling of fractured femur bone. Mater. Today: Proc.
**2020**, 22, 649–653. [Google Scholar] [CrossRef] - Czarnecki, S. Isotropic Material Design. Comput. Methods Sci. Technol.
**2015**, 21, 49–64. [Google Scholar] [CrossRef][Green Version] - Ahn, S.H.; Montero, M.; Odell, D.; Roundy, S.; Wright, P.K. Anisotropic Material Properties of Fused Deposition Modeling ABS. Rapid Prototyp. J.
**2002**, 8, 248–257. Available online: https://www.emerald.com/insight/content/doi/10.1108/13552540210441166/full/html?casa_token=NZHMQUutX98AAAAA:hAYM9lDkITmpgApyvA6h8q_71p3ZWU2WNHJ1ZehYC_IHR3Ugx2JUj_PFYK9gqCBQH6lPnW9inX6ALxehn6Op3vTzuR0KHOpDbMX0JAj1zv2oWZy_ (accessed on 20 January 2023). [CrossRef][Green Version] - Peng, L.; Bai, J.; Zeng, X.; Zhou, Y. Comparison of isotropic and orthotropic material property assignments on femoral finite element models under two loading conditions. Med. Eng. Phys.
**2006**, 28, 227–233. [Google Scholar] [CrossRef] - Dec, P.; Modrzejewski, A.; Pawlik, A. Existing and Novel Biomaterials for Bone Tissue Engineering. Int. J. Mol. Sci.
**2023**, 24, 529. [Google Scholar] [CrossRef] - Petrakis, N.L. Temperature of Human Bone Marrow. J. Appl. Physiol.
**1952**, 4, 549–553. [Google Scholar] [CrossRef] - Mirzaali, M.J.; Schwiedrzik, J.J.; Thaiwichai, S.; Best, J.P.; Michler, J.; Zysset, P.K.; Wolfram, U. Mechanical properties of cortical bone and their relationships with age, gender, composition and microindentation properties in the elderly. Bone
**2016**, 93, 196–211. [Google Scholar] [CrossRef] - Katsamanis, F.; Raftopoulos, D.D. Determination of mechanical properties of human femoral cortical bone by the Hopkinson bar stress technique. J. Biomech.
**1990**, 23, 1173–1184. [Google Scholar] [CrossRef] - Bryant, J.D.; David, T.; Gaskell, P.H.; King, S.; Lond, G. Rheology of Bovine Bone Marrow. Proc. Inst. Mech. Eng. Part H J. Eng. Med.
**1989**, 203, 71–75. [Google Scholar] [CrossRef] - Geraldes, D.M.; Phillips, A.T.M. A comparative study of orthotropic and isotropic bone adaptation in the femur. Int. J. Numer. Methods Biomed. Eng.
**2014**, 30, 873–889. [Google Scholar] [CrossRef][Green Version] - Bryant, J.D. On the Mechanical Function of Marrow in Long Bones. Eng. Med.
**1988**, 17, 55–58. [Google Scholar] [CrossRef] - Saito, H.; Lai, J.; Rogers, R.; Doerschuk, C.M. Mechanical properties of rat bone marrow and circulating neutrophils and their responses to inflammatory mediators. Blood
**2002**, 99, 2207–2213. [Google Scholar] [CrossRef][Green Version] - Zhong, Z.; Akkus, O. Effects of age and shear rate on the rheological properties of human yellow bone marrow. Biorheology
**2011**, 48, 89–97. [Google Scholar] [CrossRef] - Winer, J.P.; Janmey, P.A.; McCormick, M.E.; Funaki, M. Bone Marrow-Derived Human Mesenchymal Stem Cells Become Quiescent on Soft Substrates but Remain Responsive to Chemical or Mechanical Stimuli. Tissue Eng. Part A
**2009**, 15, 147–154. [Google Scholar] [CrossRef] - Lai-Fook, S.J.; Hyatt, R.E. Effects of age on elastic moduli of human lungs. J. Appl. Physiol.
**2000**, 89, 163–168. [Google Scholar] [CrossRef][Green Version] - Rashid, B.; Destrade, M.; Gilchrist, M.D. Influence of preservation temperature on the measured mechanical properties of brain tissue. J. Biomech.
**2013**, 46, 1276–1281. [Google Scholar] [CrossRef][Green Version] - Melo, E.; Cárdenes, N.; Garreta, E.; Luque, T.; Rojas, M.; Navajas, D.; Farré, R. Inhomogeneity of local stiffness in the extracellular matrix scaffold of fibrotic mouse lungs. J. Mech. Behav. Biomed. Mater.
**2014**, 37, 186–195. [Google Scholar] [CrossRef] - Miller, K.; Chinzei, K.; Orssengo, G.; Bednarz, P. Mechanical properties of brain tissue in-vivo: Experiment and computer simulation. J. Biomech.
**2000**, 33, 1369–1376. [Google Scholar] [CrossRef] - Booth, A.J.; Hadley, R.; Cornett, A.M.; Dreffs, A.A.; Matthes, S.A.; Tsui, J.L.; Weiss, K.; Horowitz, J.C.; Fiore, V.F.; Barker, T.H.; et al. Acellular Normal and Fibrotic Human Lung Matrices as a Culture System for In Vitro Investigation. Am. J. Respir. Crit. Care Med.
**2012**, 186, 866–876. [Google Scholar] [CrossRef][Green Version] - Chatelin, S.; Constantinesco, A.; Willinger, R. Fifty years of brain tissue mechanical testing: From in vitro to in vivo investigations. Biorheology
**2010**, 47, 255–276. [Google Scholar] [CrossRef]

Young’s Moduli (MPa) | Shear Moduli (MPa) | Poisson’s Ratios |
---|---|---|

E_{1} = 1352 | G_{12} = 292 | V_{12} = 0.30 |

E_{2} = 968 | G_{23} = 370 | V_{23} = 0.30 |

E_{3} = 676 | G_{13} = 505 | V_{13} = 0.30 |

Young’s Moduli (MPa) | Shear Moduli (MPa) | Poisson’s Ratios |
---|---|---|

E_{1} = 1352 | G_{12} = 399 | V_{12} = 0.30 |

E_{2} = 822 | G_{23} = 370 | V_{23} = 0.30 |

E_{3} = 822 | G_{13} = 399 | V_{13} = 0.30 |

Young’s Moduli (GPA) | Poisson’s Ratios |
---|---|

E_{1} = 1 | V_{12} = 0.30 |

Elastic Modulus (MPa) | Tangent Modulus (MPa) | Poisson’s Ratios | Yield Stress (MPa) |
---|---|---|---|

E = 1000 | E_{tan} = 1000 | 0.3 | 7.5 |

Young’s Moduli (GPa) | Shear Moduli (GPa) | Poisson’s Ratios |
---|---|---|

E_{1} = 16 | G_{12} = 3.2 | V_{12} = 0.30 |

E_{2} = 6.88 | G_{23} = 3.6 | V_{23} = 0.45 |

E_{3} = 6.30 | G_{13} = 3.3 | V_{13} = 0.30 |

Young’s Moduli (GPa) | Shear Moduli (GPa) | Poisson’s Ratios |
---|---|---|

E_{1} = 16 | G_{12} = 3.3 | V_{12} = 0.30 |

E_{2} = 6.30 | G_{23} = 3.6 | V_{23} = 0.45 |

E_{3} = 6.30 | G_{13} = 3.3 | V_{13} = 0.30 |

Young’s Moduli (GPa) | Poisson’s Ratios |
---|---|

E_{1} = 16 | V_{12} = 0.36 |

Elastic Modulus (GPa) | Tangent Modulus (MPa) | Poisson’s Ratios | Yield Stress (MPa) |
---|---|---|---|

E = 16 | E_{tan} = 800 | 0.36 | 108 |

**Table 9.**Effective Young’s Modulus comparisons for samples from the same bone using in vitro methods.

Marrow Sample Temperature | Rheology (kPa) | Indentation (kPa) | Cavitation (kPa) |
---|---|---|---|

25 °C | 20 °C | 20 °C | |

1 | 52.1 ±10.2 | 30.3 ± 4.0 | 64.3 ± 0.2 |

2 | 4.0 ± 0.9 | 5.7 ± 0.3 | 9.0 ± 0.01 |

3 | 0.7 ± 0.3 | 0.9 ± 0.2 | 0.9 ± 0.2 |

4 | 3.2 ± 1.9 | 2.1 ± 0.3 | 14.4 ± 10.0 |

5 | 84.4 ± 6.5 | 35.3 ± 4.9 | no data |

6 | 135.6 ± 25.6 | 37.1 ± 6.3 | no data |

7 | 69.0 ± 21.4 | — | — |

8 | — | 12.2 ± 2.8 | — |

9 | — | — | 16.0 ± 1.6 |

Average | 38.77 | 13.73 | 11.52 |

**Table 10.**Hip contact forces’ resulting components (F

_{r}, F

_{x}, F

_{y}, and F

_{z}) in (%BW) were predicted to have the following values for isotropic and orthotropic models.

Forces | Material | F_{y} | F_{z} | F_{r} |
---|---|---|---|---|

Predicted | Isotropic | 59 | − 319 | 73 |

Orthotropic | 53 | − 306 | 71 |

**Table 11.**For the first third (0–33%), the last third (66–100%), and the entire width (0–100%) of the slice, the root mean squared error (RMSE,%) and Pearson’s product-moment coefficient (r, p 0.0001) between the two distinct predictions (isotropic and orthotropic) and the CT scan profiles were calculated.

Slice | Region | Model | 0–100% | 0–33% | 66–100% | |||
---|---|---|---|---|---|---|---|---|

RMSE (%) | r | RMSE (%) | r | RMSE (%) | r | |||

1 | 5% femoral head | Iso | 32.48 | 0.49 | 17.31 | 0.77 | 22.90 | − 0.12 |

Ortho | 29.23 | 0.49 | 17.08 | 0.77 | 20.74 | − 0.02 | ||

2 | 20% shaft | Iso | 75.83 | 0.74 | 43.09 | 0.77 | 57.81 | 0.59 |

Ortho | 51.27 | 0.88 | 25.92 | 0.88 | 38.92 | 0.72 | ||

3 | 40% shaft | Iso | 107.50 | 0.29 | 65.73 | 0.37 | 78.23 | − 0.66 |

Ortho | 82.32 | 0.54 | 35.04 | 0.72 | 64.87 | − 0.09 | ||

4 | 60% shaft | Iso | 63.95 | 0.67 | 28.38 | 0.86 | 55.40 | 0.37 |

Ortho | 64.03 | 0.65 | 36.38 | 0.89 | 48.41 | 0.74 | ||

5 | 80% shaft | Iso | 72.34 | 0.53 | 34.80 | 0.73 | 53.69 | 0.60 |

Ortho | 68.29 | 0.46 | 27.07 | 0.69 | 51.83 | 0.81 | ||

6 | 95% shaft | Iso | 66.15 | 0.43 | 30.57 | 0.85 | 42.81 | 0.64 |

Ortho | 66.10 | 0.25 | 21.43 | 0.89 | 45.24 | 0.80 | ||

7 | Neck | Iso | 25.65 | 0.72 | 18.53 | 0.89 | 17.21 | 0.68 |

Ortho | 12.29 | 0.88 | 9.56 | 0.93 | 5.38 | 0.89 | ||

8 | Greater trochanter | Iso | 26.67 | 0.58 | 22.48 | 0.82 | 12.47 | − 0.14 |

Ortho | 30.72 | 0.55 | 26.08 | 0.81 | 14.90 | − 0.13 | ||

9 | Femoral head | Iso | 30.06 | 0.40 | 23.60 | 0.46 | 16.81 | 0.26 |

Ortho | 25.87 | 0.50 | 19.31 | 0.40 | 15.98 | 0.24 | ||

10 | Femoral head | Iso | 28.72 | 0.55 | 20.48 | 0.73 | 17.35 | 0.17 |

Ortho | 24.53 | 0.60 | 18.01 | 0.73 | 14.25 | 0.24 | ||

11 | Femoral shaft | Iso | 82.43 | 0.57 | 45.73 | 0.67 | 63.81 | 0.10 |

Ortho | 65.87 | 0.69 | 32.45 | 0.83 | 50.73 | 0.46 | ||

12 | Femoral condyles | Iso | 69.25 | 0.48 | 32.69 | 0.79 | 48.25 | 0.62 |

Ortho | 67.20 | 0.35 | 24.25 | 0.79 | 48.54 | 0.80 | ||

13 | Whole femur | Iso | 55.63 | 0.54 | 31.61 | 0.72 | 39.70 | 0.25 |

Ortho | 47.79 | 0.58 | 24.21 | 0.77 | 34.03 | 0.44 |

Material Properties | Elastic Bending Stiffness of the Bone | Elastic Torsion Stiffness of the Bone |
---|---|---|

Isotropic | 267 | 19.4 |

Orthotropic | 278 | 11.6 |

Anisotropic | 278 | 11.6 |

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**MDPI and ACS Style**

Bazyar, P.; Baumgart, A.; Altenbach, H.; Usbeck, A.
An Overview of Selected Material Properties in Finite Element Modeling of the Human Femur. *Biomechanics* **2023**, *3*, 124-135.
https://doi.org/10.3390/biomechanics3010012

**AMA Style**

Bazyar P, Baumgart A, Altenbach H, Usbeck A.
An Overview of Selected Material Properties in Finite Element Modeling of the Human Femur. *Biomechanics*. 2023; 3(1):124-135.
https://doi.org/10.3390/biomechanics3010012

**Chicago/Turabian Style**

Bazyar, Pourya, Andreas Baumgart, Holm Altenbach, and Anna Usbeck.
2023. "An Overview of Selected Material Properties in Finite Element Modeling of the Human Femur" *Biomechanics* 3, no. 1: 124-135.
https://doi.org/10.3390/biomechanics3010012