Structured deformation of damaged continua with cohesive-frictional sliding rough fractures

The influence of cohesive-frictional crack sliding on the response of quasi-brittle fractured bodies and, in particular, the shear-induced dilatation due to crack surmounting, are here considered by assuming an equivalent shape function for crack-lip roughness. The deformation is modeled at the continuum level via structured deformation theory, introducing relevant kinematical descriptors that are now set in the classical thermodynamic formulation for generalized standard materials. The resulting model lies in the “simplified model” class, since internal variables may be reduced to one scalar parameter associated with the smeared-crack slip. Remarkably, even in the presence of friction, the structured-deformation approach renders the model fully-associated in type, a property particularly relevant for F.E. implementation. In the simplest case no evolution of crack density and orientation is supposed, and despite this simplification, a good description of the response of cracked masonry or concrete walls under seismic-like shear are provided by the model, whose calibration is obtainable through ad hoc tests. Interesting instabilities in the shearing path are exhibited, suggesting as well a possible generalization of the Mohr–Coulomb criterion.