A Continuum Model with an Embedded Fracture Process Zone Modelled as a Cohesive Frictional Interface

Failure in quasi-brittle materials, such as concrete and rock, usually develops in a fracture process zone (FPZ), in which dissipative processes takes place. At the onset of bifurcation or upon formation of FPZ the homogeneity of kinematic fields is lost and the stress field is redistributed which gives rise to the so called deterministic size effect problem. The total strain energy stored within a specimen of quasi-brittle materials will scale with its size; however, the amount of dissipated energy does not depend on the specimen size but only on the width of the FPZ. This width is related to the microstructure of the material and is considered a characteristic of the material. In this paper, a cohesive frictional interface is used to model the dissipative behaviour of material inside FPZ. Fundamental micro-mechanisms of energy dissipation such as micro-crack opening in mode I and frictional sliding between micro-crack surfaces are formulated within the frame work of Thermodynamic with internal variables (TIV) to ensure the thermodynamics admissibility of the model. The link between the material behaviour inside and outside FPZ is given through the continuity of tractions along the boundaries of FPZ. It is shown that although the shape of the post-peak stress-strain varies, for specimens of different slenderness, the amount of dissipated energy remains the same in all cases.