The effects of interphase and bonding on the elastic modulus of bone: changes with age-related osteoporosis

A simple shear lag model is developed to analyze the physics of the stress transfer between the organic and mineral constituents of bone tissue in the presence of an interphase and changes in bonding. The analytical model is developed assuming interactions between overlapped bone mineral platelets. The platelets are assumed to carry the axial stresses while the organic matrix transfers the stresses from one platelet to another by shear. A decrease in the interphase mechanical properties decreases the elastic modulus due to increased shear between the overlapped platelets. A decrease in bonding decreases the elastic modulus due to an increase in the axial stress transferred from the ends of the platelet. The implications of the changes in parameters on the age-related disorders of bone (osteoporois) are discussed. It is suggested that the aspect ratio and volume fraction of the mineral in the remaining bone tissue would increase due to a reduction in the density of the bone. The mechanical properties of the organic are hypothesized to increase due to a reduction in the density of bone leading to an increased tendency for damage within the organic.