Keywords: continuum damage, bone, femur, finite element, von-Mises, human femur.

In this article by employing the principle of continuum damage mechanics and solving the governing equations using the finite element (FE) technique, the damage process in a composite media like a human long bone has been studied. To do this, primarily a CT scan of a femur is converted to proper model usable for a FE model. After applying load incrementally of a monotonic nature, the state of stress or strain in each element and consequently in the medium are calculated using finite element software. Based on the principle of continuum damage and the value of stress in each element, the damage rate is calculated and the mechanical properties at that point are updated for the next step of loading. This process goes on until the inception of the failure at a critical point. It is noted that the femur neck region is the most critical zone for growth of the damage in a standing position. The damage initially starts from lower part of femur and in continuation, the upper part of femur experiences more sever damage effect.

Carter et al. [1] performed the primary fundamental works in the study of damage in the bones. They succeeded to observe the phenomenon of microscopic damage due to cyclic loading. In 1986, Corondan and Harworth [2] used electron microscope and the fractography principle to study the pre-fracture phenomenon in the bone. In 1987, Krajcinovic [3] presented a model for growth of the damage in cortical bone. It has to be mentioned that the induced damage due to high strain rate loads, massive amount of damage will be generated in a short time and there will not be enough time for the bone to heal from this damage [4].

A study of the experimental results indicates that before bone final rupture, considerable microscopic damage will be accumulated at the sub-structural level. By employing laser scanning techniques, microscopic cracks with a size of 1μm to 10μm are detected in the fractured zone of the bone. More study indicates that microscopic cracks with different intensity are spread in all points under stress. Hence, under these conditions, utilizing the theory of continuum damage mechanics is permissible [5]. By implementing models for damage growth in this paper, a study of the damage growth process in a femur under increasing monotonic loading is presented.

The first step in solving the damage growth relations numerically in a human femur is to establish a 3D finite element model. To do this, following steps are considered:

1. Preparing a proper FE model from the geometry of the bone using computer tomography scanning technique.
2. Selecting suitable elements and applying boundary conditions using the FE software.

The chosen element for this study is the eight-nodded solid brick type with three DOF at each node. The shape of human femur was generated using the AutoCAD software and the assembled FE model of a human femur comprised a total number of 7908 elements and 9906 nodes.

In this paper, the phenomenon of damage initiation and its growth in a human femur under increasing monotonic axial load using the theory of continuum damage mechanics is studied numerically. To do this the FE model of the femur is constructed using CT scan imaging. A computer program is written capable of conducting the damage calculations based on different damage growth models under increasing monotonic loading.

Based on numerical results it is seen that the femur neck area for a loading similar to standing position is at maximum damage distribution and ultimately fracture. More specifically in daily life this section is more vulnerable to being attacked by different diseases like bone resorption and cancer causing appreciably strength reduction. In this study, it is also noted that the damage starts from the lower cortical part of the bone neck and it progresses more rapidly with a higher rate to the upper part of the neck. Also, it is observed that the cortical part of bone in the ephiphysis area plays not only an important role in the strengthening of this area but acts as a bypass zone such that it reduces the transferring forces to the trabecular part of the bone, i.e. it protects this zone as a shield from any damage and further fracture.

1

D.R., Carter, W.C., Hayes, and D.J., Schurman, "Fatigue Life Of Compact Bone", Journal Biomechanics, 9, 211-218, 1976. doi:10.1016/0021-9290(76)90006-3

2

G., Corondan and W., Haworth, "A Fractographic Study of Human Long Bone", Journal Biomechanics, 19, (3), 207-218, 1986. doi:10.1016/0021-9290(86)90153-3

3

D., Krajcinovic, J., Trafimow and D., Sumarac, "Simple Constitutive Model for a Cotical Bone", Journal Biomechanics, 20, (8), 770-784, 1987. doi:10.1016/0021-9290(87)90057-1

4

P.J., Prendergast, and R., Huiskes, "Micro Damage and Osteocyte Lacuna Strain in Bone: A micro Structure, Finite Element Analysis", ASME Journal of Biomechanical Eng., 118, 240-245, 1996. doi:10.1115/1.2795966

5

P., Zioupos, X. T., Wang, and J. D., Currey, "Experimental and Theoretical Quantification of the Development of Damage in Fatigue Test of Bone and Antler", Journal Biomechanics, 29, 989-1002, 1996. doi:10.1016/0021-9290(96)00001-2

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