Multiscale modeling of bone
Clumpner, Brandon R.
Kwon, Young W.
Didoszak, Jarema M.
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A multiscale model was developed to link the hierarchies of human bone in different length scales. Bone has a unique structure displaying large stiffness with minimal weight. This is achieved through a hierarchy of complex geometries composed of only three materials: hydroxyapatite, collagen and water. The identifiable structures of bone are hydroxyapatite, tropocollagen, fibrils, fibers, lamellar layers, trabecular bone, cancellous bone and cortical bone. A spring model was used to evaluate the stiffness of collagen. A unit-cell based micromechanics model analyzed both the normal and shear properties of fibrils, fibers, and lamellar layers. A layered composite model assessed cortical and trabecular bone while a simple finite element model was used to evaluate cancellous bone. Modeling bone from nanoscale components to macroscale structures allows the influence of each structure to be assessed. It was found that the distribution of hydroxyapatite within the tropocollagen matrix at the fibril level influences the macroscale properties the most. Additionally, the model allows perturbations to the geometry of any hierarchy to be analyzed. With so little known about the detailed structure of nanoscale and microscale bone, a model comprising the complete hierarchy of bone can be used to help validate assumptions or hypotheses about structure.
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