Effect of relative stress on post-peak uniaxial compression fracture energy of concrete

Fracture energy in strain softening regime was investigated analytically by considering microstructures interaction and interplay. Based on gradient-dependent plasticity, the thickness of localized band was determined completely and strictly by characteristic length in relation to average grain diameter. After obtaining the plastic shear displacement of the band, the formula on axial response of concrete was proposed and the analytical post-peak fracture energy was deduced. A comparison between present theoretical results and earlier experimental results was carried out and the analytical result is reasonable and has a plausible foundation as considering the localized failure theoretically. Decreasing the relative stress leads to increasing the fracture energy non-linearly. The large the shear elastic modulus and shear softening modulus, the lower the post-peak fracture energy. A larger fracture energy is caused by a larger thickness of shear band or a larger characteristic length of concrete material. If the inclination angle of the shear band and the compressive strength are not concerned with structural size of specimen, the post-peak fracture energy is size independent.