A unified stochastic damage model for concrete based on multi-scale energy dissipation analysis

This work proposes a unified damage model for concrete within the framework of stochastic damage mechanics. Based on the micro-meso stochastic fracture model (MMSF), the nonlinear energy dissipation process of the microspring from nanoscale to microscale is investigated. In nanoscale, the rate process theory is adopted to describe the crack growth rate; therefore, the corresponding energy dissipation caused by a representative crack propagation can be obtained. The scale gap from nanoscale to microscale is bridged by a crack hierarchy model. Thus, the total energy dissipated by all cracks from the nanoscale to the microscale is gained. It is found that the fracture strain of the microspring can be derived from the above multi-scale energy dissipation analysis. When energy dissipation is regarded as some microdamage to the microspring, the constitutive law of the microspring is no longer linearly elastic, as previously assumed. By changing the expression of the damage evolution law from fracture strain to energy dissipation threshold, the new damage evolution model is derived. The proposed model can not only replicate the original static model but also extend to cases of rate dependence. By deriving the fracture strain under different strain rates, the rate sensitivity of concrete materials can be reflected. The model parameters can be conveniently obtained by identifying them with experimental data. Finally, several numerical examples are presented to verify the proposed model.