A NEW STOCHASTIC DAMAGE CONSTITUTIVE MODEL OF CONCRETE CONSIDERING STRAIN RATE EFFECT

Due to the complex and randomly distributed components of concrete materials, the mechanical behavior of concrete materials inevitably exhibits nonlinearity and randomness. In addition, the mechanical properties of concrete materials are sensitive to strain rates. This work established the nano-micro-meso stochastic damage model to comprehensively reflect the three basic properties of nonlinearity, randomness, and strain rate sensitivity in the mechanical behavior of concrete. By introducing the rate process theory to describe the growth rate of nano-cracks, the related energy dissipation process can be obtained. The nanoscale analysis is upscaled to the micro scale by a crack hierarchy model, and the expression for micro energy dissipation is derived. The nano-micro-meso stochastic damage constitutive model for concrete was established by combining the micro energy dissipation expression with the micro-meso stochastic fracture model. In the meantime, a time-dependent energy barrier is used for analyzing the bond surviving probability under different loading rates. Assuming the evolution of reaction coordinate is governed by the Langevin equation, the surviving probability can be obtained by solving the corresponding Fokker-Planck-Kolmogorov equation. The results reveal that the increase of dynamic strength resulted from the competitive mechanism of loading rate and bond breaking rate. Since the first eigenvalue of the Fokker-Planck-Kolmogorov equation corresponds to the rate process theory, it is not applicable when the loading rate is too high. According to the analysis aforementioned, it is assumed that the interaction between micro-cracks is linearly related to the corresponding logarithmic strain rate, so the energy dissipation rate of the micro-spring is related to the strain rate, extending from the static constitutive model to the dynamic constitutive model. Numerical examples show that the proposed model can simultaneously reflect the nonlinearity, randomness, and strain rate sensitivity in the mechanical behavior of concrete materials. The correctness of the proposed model is verified by comparison with the relevant experimental results.