A Fractal Analysis of the Size Effect in Quasi-Brittle Materials: Experimental Tests and Peridynamic Simulations

In the design of structures involving quasi-brittle materials such as concrete, it is essential to consider the scale dependence of the mechanical properties of the material. Among the theories used to describe the phenomenon of size effect, the fractal theory proposed by Carpinteri and colleagues has attracted attention for its results in the last three decades of research. The present study employs the fractal perspective to examine the scale effect in three-point bending tests conducted on expanded polyethylene (EPS) beam specimens. The influence of size on flexural strength, fracture energy, and critical angle of rotation is investigated. Additionally, numerical simulations based on peridynamic (PD) theory are performed based on the experimental tests. The global behavior, brittleness, failure configuration, and fractal scale effect obtained numerically are evaluated. The numerical results show a good correlation with the experimental ones and, moreover, both the experimental and numerical results are in agreement with the fractal theory of scale effect. More precisely, the error of the sum of the fractal exponents, computed with respect to the theoretical one, is equal to −1.20% and −2.10% for the experimental and numerical results, respectively. Moreover, the classical dimensional analysis has been employed to demonstrate that the scale effect can be naturally described by the PD model parameters, allowing to extend the results for scales beyond those analyzed experimentally.