Minimum energy based method to predict the multiple cracking pattern in quasi-brittle beam

A minimum energy based method is proposed to predict the evolution of multiple cracking pattern in a pure bending beam made of quasi-brittle material. The minimum energy is found from the energy landscape of the cracked beam calculated by the Finite Element (FE) Method, and the crack pattern corresponding to the minimum energy is taken as the crack pattern most likely to occur. The fracture behavior of the quasi-brittle material is simulated by cohesive zone model (CZM) using the bilinear tension softening law. After appropriate normalization based on dimensional analysis, the multiple cracking process is found to be governed by only three parameters and their effects are systematically studied. Physically, the ratio between the “crack-tip toughness” and the “bridging toughness” is important for the crack pattern evolution. As a validation, the proposed method is used to predict the crack pattern of fiber reinforced concrete beam and good agreement with experiment is achieved. The goal of this paper is twofold. First, with a systematic parametric study focusing on the constitutive law of quasi-brittle material, this investigation would facilitate material design or selection for crack control; Second, by quantitatively determining the crack pattern development during the whole multiple cracking process based on a sound physical principle, i.e., the commonly adopted minimum energy criterion, the result can serve as a benchmark for checking the reliability of other methods for multiple cracking analysis.