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Analytical Solutions of the Displacement and Stress Fields of the Nanocomposite Structure of Biological Materials

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                                            Gang Liu1,3, Baohua Ji1,2†, Keh-Chih Hwang1†, Boo Cheong Khoo3[1] 

                                           1 AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China2 Biomechanics and Biomaterials Laboratory, Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China3Singapore -MIT Alliance, Department of Mechanical Engineering, National University of Singapore, Kent Ridge, Singapore 119260, Singapore

[1] Corresponding authors: Email: (BJ); (BCK); (KCH) 

ABSTRACT: Biological materials such as bone, teeth 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 generic nanocomposite structure. 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 (GAMA) 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 (GAMA) 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, etc., of biological materials.


Kmomeni's picture


I looked at your manuscript and I have a question about it.  I was wondering how different it is compared to the shear-lag model introduced by Cox in 1952 or this one: Gao, X., & Li, K. (2005). A shear-lag model for carbon nanotube-reinforced polymer composites. International Journal of Solids and Structures, 42(5-6), 1649-1667. doi:10.1016/j.ijsolstr.2004.08.020



LG's picture

Hai, Thanks for your query. Actually, in our paper, basing on the perturbation methods, we gave a more precise equivalent Yong's modulus. Furthermoew, we obtained the detailed stress and displacement formulas of the staggered mineral-protein composites under external tension, that are the Shear-leg model can not supply.

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