Modeling tensile damage and fracture of quasi-brittle materials using stochastic phase-field model

Abstract

In this paper, a stochastic phase-field model is presented to simulate the nonlinearity and randomness of the mechanical behaviors of quasi-brittle materials within a unified macroscopic continuum framework. By characterizing the spatial variations in material failure strength and fracture toughness for fully correlated random fields, a complete theoretical framework of the stochastic phase-field model is established, and a corresponding numerical analysis program is proposed. In particular, this model is used with the probability density evolution theory to derive the probability density function of the mechanical response. Numerical results show the effect of material randomness on the failure patterns and macroscopic responses of quasi-brittle media under tension. Comparisons between the experimental and numerical results demonstrate the effectiveness of the proposed model in replicating the probabilistic information of macroscopic responses of random quasi-brittle structures. Furthermore, the effects of autocorrelation length on probabilistic failure of quasi-brittle media are investigated by the stochastic analysis of a three-point bending beam.