Couple effect of surface energy and strain gradient on the mechanical behaviors of the biological staggered composites

Abstract

Biological staggered composites, which are hierarchy spanning from nano scale to macro scale, boast remarkable mechanical properties. In this paper, a trans-scale shear-lag model is established based on the strain gradient theory and the Gurtin-Murdoch model, which provides a chance to glimpse how the micro-nano structures of the biological composite determine its macroscopic mechanical behavior. With the trans-scale shear-lag model, we found that the deformation, stress distribution and overall effective modulus have strong size effects, which are related to the thickness of the ‘matrix’ and ‘platelet’ of the biological staggered composites. Based on the analysis, two normalized numbers d/l and Es/(hEp) are proposed to describe the size effects caused by the thickness of the matrix and platelet, respectively. Besides, the predicted effective moduli of the biological staggered structure composites are compared with the experiments to verify our trans-scale shear-lag model. Our research sheds light on the understanding of the mechanical behaviors of the staggered biological composites and provides theoretical guidance for the design of high-performance bionic composite materials.