Describing the stress–crack-opening relationship using a three-exponential model

The paper reports on a proposed simple mathematical function to describe the strain–softening behaviour observed in uniaxial tensile tests on a wide range of concretes. Two mathematical functions—a linear-double-e and a three-e model—are proposed which are able to describe such curves via one continuous function and thus have the advantage of being mathematically efficient. The proposed functions have been compared with actual uniaxial tensile test results on both plain and steel-fibre-reinforced concrete. Both qualitative and quantitative results show that the three-e model can accurately describe the strain–softening curves for a wide range of concrete strengths. In addition, a systematic procedure is reported whereby model parameters are determined objectively.