Hysteretic deteriorating model for quasi-brittle materials based on micromechanical damage approach

A damage model, which is based on the stochastic modeling of the microstructures, is developed for the quasi-brittle materials subjected to repeated loading. According to this model, the overall response of the material is represented with a series of micro-elements joined in parallel. A combined model is proposed for the micro-element considering the fracture as well as the hysteretic energy dissipation. To account for the progressive failure, the random fracture strains are assigned to the micro-elements. Therefore the overall parallel bundle is considered as a stationary random field. Then by averaging the microscopic random field, the overall loading, unloading and reloading curves are derived analytically. Two hysteretic rules are derived from the proposed model, and the overall hysteretic deteriorating behaviors could be well reproduced. To demonstrate the validity of the present model, the numerical results are shown against the stochastic simulated curves as well as the experimental data. The present model provides an alternative approach for the efficient modeling of the hysteretic deteriorating behaviors for the quasi-brittle materials.