Scaling Effect for Tensile Properties of Cementitious Materials Based on Self-Similarity: From Nano to Macro

Abstract

Cementitious materials contain multiple phases, from the nanoscale to the macroscale. Although different mechanical properties are observed at each scale length, similarities can still be found in their spatial structural features and in the geometry of the stress–strain curves over various scales. This study aims to provide a quantitative description of the scaling effect based on the concept of self-similarity. Multiscale models are proposed for the tensile strength, peak strain, and elastic modulus of cementitious materials. The results obtained from these models exhibit a change of five orders of magnitude in tensile strength as the scale length increases from 10−9 m to 100 m, whereas a slight decrease in the elastic modulus is observed. Combined with the models above and the Morse function, a continuous constitutive model is proposed to describe the tensile stress–strain behavior at each scale length. This paper studied the scale effect of cementitious materials from the viewpoint of self-similarity and investigated this phenomenon over a very broad length range, including the nano-, micro-, meso-, and macro-scale. The tensile stress–strain relationship was unified and characterized across scales, which not only reflected the atomic interaction on the nanoscale via the Morse potential energy function, but also depicted the macroscopic tensile tests results. These findings provide new insights in revealing the mechanism of quasi-brittle materials’ size effect.