Mechanical behavior and size effect of the staggered bio-structure materials


The recent advancement in technology has seen the development of advanced bio-compatible materials suitable for various applications. For instance, natural biomaterial such as bones are generally made of minerals and organics at micron scale. Thus, owing to the different properties of organic and minerals components, the resulting composite exhibit excellent mechanical properties such as stiffness and toughness. Consequently, their hierarchical microstructure is the key contributor to the enhanced properties at macroscopic scale. This has attracted significant attention of researchers who have continued investigating the staggered biomaterials. Unfortunately, the relationship between the microstructures and mechanical properties of the biomaterials have not been fully explored.

Presently, several mechanical models have been developed to investigate the relationship between the properties and microstructure of biomaterials. For example, the brick and mortar model majorly used in the examination of the nacre involves the inclusion of the actual microstructure observations. Consequently, the staggered array-based mechanical model tokes into consideration the tensile and shear deformations of the organic matrix. Remarkably, nearly all of the developed mechanical models give the key characteristics of the staggered structure. Unfortunately, they do not give effects of the microstructure features and nanoscale characteristics.

The researchers of Professor Wei Yueguang’s group at Peking University and at Chinese Academy of Sciences developed a trans-scale shear-lag model to characterize the mechanical properties and size effects of staggered biomaterials. They considered the organic materials as elastic strain gradient continuum while the mineral platelets were treated as classical elastic materials. The purposed to obtain the elastic fields and analytical expressions of the effective modulus of the staggered biomaterial under investigation. Their research work is currently published in the research journal, Mechanics of Materials.

From the experimental results, the authors observed that for the staggered bio-structure material, the mechanical behavior exhibited the strongest size effects. Consequently, the analytical expressions of the overall effective modulus deformations and interfacial strengths were successfully obtained. Furthermore, it was necessary to use a combination parameter to describe the size effects. The parameters included the organic material layer thickness, material length among others. Therefore, an increase in the combination parameter resulted in a corresponding decrease in the interfacial strength and overall effective modulus while it considerably led to a decrease in the interfacial deformation.

The developed method is suitable for several lengths of the bio-structured material from nanoscale to microscale thus enabling characterization of the small features that play a significant role in determining the properties of such materials. In addition, thin organic layers led to rapid strain changes hence strong strain gradient effects.

The authors successfully constructed a mechanical model that took into consideration the effects of the microstructure as well as the scale. Thus, it can be conveniently used for staggered biomaterials with small modulus ration of organic mixture to mineral platelets and also small aspect ratio. The consistency of the predicted moduli for different shells confirms the accuracy and functionality of the model. As such, it will advance mechanical properties for biomaterials for numerous applications.

About the author

Yueguang Wei, Boya Chair Professor at Peking University and a Fellow of the Chinese Academy of Sciences, graduated from the Department of Mechanics of Tsinghua University with a ph.D. degree of solid mechanics in July 1992. He was a Post-Doctoral Fellow at Harvard University from January 1995 to August 1998, and a professor at the Institute of Mechanics of the Chinese Academy of Sciences from August 1998 to November 2016. He was a visiting professor at Harvard University from August 2000 to March 2001. From November 2016 to the present, he is a Boya Chair Professor of Peking University. His main research interests are the trans-scale mechanics of solids, elastoplastic fracture mechanics, composite mechanics and so on.


Ma, H., Wei, Y., Song, J., & Liang, L. (2018). Mechanical behavior and size effect of the staggered bio-structure materialsMechanics of Materials, 126, 47-56.

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