Crack band theory for fracture of concrete

A fracture theory for a heterogeneous aggregate material which exhibits a gradual strain-softening due to microcracking and contains aggregate pieces that are not necessarily small compared to struttural dimensions is developed. Only Mode I is considered. The fracture is modeled as a blunt smeared crack band, which is justified by the random nature of the microstructure. Simple triaxial stress-strain relations which model the strain-softening and describe the effect of gradual microcracking in the crack band are derived. It is shown that it is easier to use compliance rather than stiffness matrices and that it suffices to adjust a single diagonal term of the compliance matrix. The limiting case of this matrix for complete (continuous) cracking is shown to be identical to the inverse of the well-known stiffness matrix for a perfectly cracked material. The material fracture properties are characterized by only three paPlameters-fracture energy, uniaxial strength limit and width of the crack band (fracture Process zone), while the strain-softening modulus is a function of these parameters. A m~thod of determining the fracture energy from measured complete stress-strain relations is ' also given. Triaxial stress effects on fracture can be taken into account. The theory is verljied by comparisons with numerous experimental data from the literature