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

Staggered structure materials, or "brick and mortar" structure materials, are widely observed in natural biomaterials. In this paper, based on strain gradient theory, a trans-scale shear-lag model is developed to characterize the mechanical properties and their size effects for the staggered bio-structure materials. The analytical expressions of the overall effective modulus, interfacial strengths and deformations of the staggered bio-structure material have been obtained. The results illustrate that the overall effective modulus, interfacial strengths and interfacial deformations have the strong size effects. These effects can be described by a combination parameter, i.e. thickness of organic material layer over the material length scale parameter of strain gradient theory. The overall effective modulus and interfacial strength increase with the decrease of the combination parameter. However, the interfacial deformation considerably decreases with the decrease of the combination parameter value. When the combination parameter value is taken as very large, corresponding to the case of large organic matrix thickness, the results return to the classical ones. The predicted effective moduli of nacre are also compared with experimental results and are in good agreement with experimental results