Multi-Scale Modeling of Human Cortical Bone: Aging and Failure Studies
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Multi-Scale Modeling of Human Cortical Bone: Aging and Failure Studies Elisa Budyn1, and Thierry Hoc2 1 Department of Mechanical Engineering, University of Illinois at Chicago, 842 West Taylor Street, Chicago, IL, 60607 2 Department of Material Science - LMSSMat, Ecole Centrale Paris, Grande Voie des Vignes, Chatenay Malabry, 92295, France
ABSTRACT A multiscale model for fracture in human cortical bone is presented. The first aspect of this study concerns the effect of aging on the structural and mechanical properties of human cortical bone using 3D FEM unit cells. The second aspect of this study is devoted to the failure mechanism and the propagation of cracks in cortical bone under tension using the eXtended Finite Element Method (XFEM), which is well suited for multiple crack growth because remeshing is avoided. The results show that the energy required to percolate cortical bone unit cells is reduced in the case of low remodeling and osteoporosis by one third and two thirds respectively. The modeling results agree with experiment. This investigation shows for the first time a quantitative correlation between the microstructure and the energy necessary to fracture cortical bone. The method opens new opportunities to characterize pathologies in cortical bone. INTRODUCTION A major concern is damage to human bone as the population is aging. Fracture risk highly increases in elderly individuals, particularly women. In this context, a multi-scale analysis of human cortical bone unit cells is presented. Experiments are conducted on bovine [1] and human specimens of different ages in order to measure relevant geometrical and mechanical parameters and obtain microscopic data that will be fed into finite element models. First, a 3D statistical FEM model was developed to faithfully replicate human cortical bones with their microstructural and mechanical specificities including possible pathologies. The continuum model computes macroscopic information that is validated through comparison with experimental measurements. Second, a 2D XFEM model was developed in order to allow the growth of multiple cracks until complete failure of the cell. An elastic-damage criterion is applied in order to place initial cracks in maximum strain locations of the strain fields resulting from the 3D continuum model. The cracks are modeled using the eXtended Finite Element Method [2, 3] and grown based on a local Griffith criterion until percolation [4]. The continuum model is applied to study the effect of aging on the structural and mechanical properties of human and bovine cortical bone. The XFEM model is applied to the failure mechanism and the development of cracks in cortical bone under tension.
DESCRIPTION OF THE MODEL The statistical FEM continuum model reconstructs three dimensional unit cells of human cortical bone with dimensions measured by microscopic observations. The size of each specimen is chosen above the RVE size to be statistically significant. Human cortical bone microstructures are represented by a four pha
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