A three-invariant cap-plasticity damage model for cementitious materials

We present a new continuum elastoplastic damage model for cementitious materials which captures their distinct behavior in tension and compression due to crack-induced damage and irreversible plastic deformation. It also describes their response under multi-axial loading with low to high confining pressures. A smooth, closed-convex three stress-invariant yield surface is developed which perpendicularly intersects the negative hydrostatic axis and is composed of a shear loading surface and an elliptical cap. It incorporates a plastic internal state variable (ISV) characterizing non-uniform hardening of both shear loading surface and elliptical cap, while the flow rule is considered to have volumetric non-associativity. Damage evolution laws incorporate two ISVs describing crack growth at the macroscale under tensile and compressive stresses separately. Overall damage under multiaxial loading explicitly considers the effect of confining stresses on damage evolution and stiffness recovery effects under cyclic loading. Model predictions are compared against several experimental results on various concretes and also against responses of recently reported models. The proposed model predicts distinctive features of concrete very well including hardening behavior in triaxial-compression and both pre- and post-peak volumetric behavior.