Analytical solutions of the displacement and stress fields of the nanocomposite structure of biological materials

Biological materials, such as bone and nacre, are nanocomposites of protein and mineral with superior mechanical properties. The basic building blocks of these materials feature a generic nanocomposite structure with staggered alignment of mineral platelets in protein matrix. Because of the structural complexity of the generic structure, its displacement and stress fields are currently still unknown. In this study, a perturbation method was applied for analytically solving the displacement and stress fields of the nanocomposite structure under uniaxial tension. The effect of the elastic modulus, aspect ratio and volume fraction of mineral and protein on the displacement and stress fields in the nanocomposite structure was studied. A non-dimensional parameter γ was then suggested for characterizing the stress and strain fields in this nanostructure. We showed that the assumption of uniform shear stress distribution at the mineral–protein interface in the TSC model is valid when γ is less than 4 which is broadly applicable to most biological materials. The analytical solutions of displacement and stress fields obtained in this study provide a solid basis for further analyses of mechanical properties, such as the buckling and the fracture behaviors of biological materials.