Isotropic damage model with different tensile-compressive response for brittle materials

Incremental constitutive equations for brittle materials are formulated on the grounds of a frictional microcracked elastic model. The hypothesis of isotropic damage and the description of normal and tangential contact tractions on the crack faces by means of two second-order tensors provide a constitutive model with a reduced number of internal variables. The evolution equations of the latter ones are deduced from frictional and damage limit states and corresponding flow rules, from which the different behaviour to tensile and compressive stress states and dissipation at constant damage are represented. The model response is analysed for different stress states and limit strength domains are derived for monotonically increasing biaxial and triaxial stress states. Comparisons of the theoretical results with experimental data from literature related to concrete and cast-iron corroborate the proposed approach