Analysis of localized cracking in quasi-brittle materials with a micro-mechanics based friction-damage approach

Abstract This paper is devoted to the study of transition from diffuse damage to localized cracking in quasi-brittle materials. A micro-mechanics based friction-damage model is first formulated with a rigorous homogenization procedure. The plastic deformation is related to the frictional sliding along diffuse micro-cracks while the damage is induced by the growth of micro-cracks. The localized cracking is considered as a consequence of coalescence of diffuse micro-cracks. The onset of localized crack is then defined by introducing a critical value of diffuse damage density parameter. The orientation of localized crack is determined from the Mohr’s maximization postulate. After the onset of a localized crack, the energy dissipation of material is entirely related to the frictional sliding and propagation of the localized crack. In this context, a localized friction damage model is developed in the framework of thermodynamics to describe the frictional sliding of the localized crack which acts as the driving force for its propagation. As an example, analytical results of localized crack angle are determined for some specific loading paths including plane stress, plane strain and conventional triaxial compression. Moreover, analytical solutions of complete stress–strain curves with the transition from diffuse damage to localized cracking are also obtained for conventional triaxial compression tests and compared with experimental data.