A novel three dimensional failure criterion for quasi-brittle materials based on multi-scale damage approach

In this paper, we propose a novel three-dimensional micromechanics-based failure criterion to assess the load-bearing capacity of quasi-brittle materials under complex multiaxial stress conditions. This criterion not only inherits benefits of the multi-scale friction-damage coupling modeling approach but also accounts for the effect of the intermediate principal stress. Physically, the initiation and propagation of microcracks contribute to the damage, and the failure of the material ultimately occurs due to the unstable growth of microcracks. Simultaneously, plastic deformation, which results from frictional sliding along microcracks, is intimately coupled with the damage process. Employing friction-damage coupling up-scale analyses and introducing a novel parabolic local frictional law, we derive a new nonlinear compression meridian criterion within the upscaling framework. Moreover, by incorporating a Lode dependence function, this criterion effectively addresses variations in strength induced by the intermediate principal stress. To validate this criterion, we utilize data from triaxial compression, triaxial extension, and true triaxial tests conducted on various rock materials and concrete, all of which demonstrate excellent agreement.