Orthotropic multisurface model with damage for macromechanical analysis of masonry structures

A novel macromechanical model with damage for the analysis of masonry structures in-plane loaded is presented. The model accounts for the directional mechanical properties typically characterizing response of masonry with regular texture. Indeed, the real heterogeneous material is modeled as a fictitious homogenized medium with orthotropic elastic constitutive behavior along the masonry natural axes, identified as the parallel and normal directions to bed joints orientation. The different strength characteristics along each material axis are taken into account by properly defining a damage matrix, which accounts for failure mechanisms due to axial tensile and compressive states, as well as shear. A suitable criterion is introduced, resulting in a damage limit surface geometrically defined in the space of the damage associated variables by the intersection of two ellipsoids and an hyperboloid. The model is implemented into a finite element procedure where the mesh-dependency numerical issue is avoided by adopting a nonlocal integral formulation. Validation examples, involving simple uni-axial and bi-axial tests, as well as more complex loading conditions, are provided to prove the model performances at both material and structural scale.