Modeling the Tensile Mechanical Behavior of Bone along the Longitudinal Direction

The tensile stress–strain behavior of bone along its longitudinal axis is modeled by using a simple shear-lag theory, wherein, stresses and strains in a unit cell consisting of an organic matrix reinforced by overlapped mineral platelets are computed. It is assumed that loads are transferred between overlapped mineral-platelets by shear in the organic matrix. The mechanical behavior of bone in which the matrix partially or completely debonds from the sides of the overlapped mineral platelets (after an ultimate interfacial shear stress value is exceeded) is modeled. It is shown that the tensile mechanical behavior of bone can be modeled only by assuming little or no debonding of the organic from the mineral. A physical phenomenon that explains the tensile behavior of bone is, after the interfacial shear stress has reached a constant value over the length of the mineral platelets, the collagen molecules/microfibrils (with the associated mineral platelets) move relative to one another. The tensile stress–strain curve of bovine bone is modeled using this model. The theory predicts the mechanical behavior of the tissue in the elastic, yield and post-yield region. The ultimate strain and strengths are not predicted in the present model.