6. Conclusions
Based on the theoretical analysis and the numerical example, several conclusions can be obtained as follows:
(1) The fiber bundle model can simulate the random fracture of concrete fibres, and a stochastic model is developed to describe the behaviour of concrete fibre at the micro-level.
(2) A probabilistic relation between the damage variable and the fibre strain is established. The damage evolution can be quantified by two random variables.
(3) The mean and standard deviation of damage evolution agree quite well with the corresponding analytical solutions. The probability density function of the damage can also be obtained.
(4) The proposed method is quite efficient for stochastic response determination and reliability evaluation of complex structures.