Transfer of shear tractions along rough cracks

A constitutive model for transfer of shear tractions along rough cracks in strain softening composites like concrete, is presented. The model relates the normal and shearing stresses on the rough crack to the corresponding displacements in terms of the interface strength, contact areas, the contact angle of the rough crack surface, and the crack closing pressure. The initial angle of contact at zero normal stresses, a fundamental property of the rough crack surface, was established by means of statistical and numerical simulations. Using the concepts of critical state soil mechanics, conditions were stipulated for dilation and contraction of the rough crack. The deformability of the asperity was mathematically described in terms of the initial angle of contact and a progression of this angle to a minimum by means of an exponential model. Using idealized test results such as constant crack width experiments, a mathematical model was developed for contact area as a function of the crack width and tangential displacement. The performance of the constitutive model was verified by predicting experimental results with varying crack width and normal stress boundary conditions, as well as constant crack width and constant normal stress. The comparison between predicted and experimental results appear to be very satisfactory.