A thermodynamic framework for the evolution of damage in concrete under fatigue

A closed-form expression for the dual of dissipation potential is derived within the framework of irreversible thermodynamics using the principles of dimensional analysis and self-similarity. Through this potential, a damage evolution law is proposed for concrete under fatigue loading using the concepts of damage mechanics in conjunction with fracture mechanics. The proposed law is used to compute damage in a volume element when a member is subjected to fatigue loading. The evolution of damage from microcracking to macrocracking of the entire member is captured through a series of volume elements failing one after the other. The number of loading cycles to failure of the member is obtained as the summation of number of cycles to failure for each individual volume element. A parametric study is conducted to determine the effect of the size of the volume element on the model's prediction of fatigue life. A global damage index is also defined, and the residual moment carrying capacity of damaged beams is evaluated. Through a deterministic sensitivity analysis, it is found that the load range and maximum aggregate size are the most influencing parameters on the fatigue life of a plain concrete beam.