Modeling of unreinforced masonry walls under shear and compression

This paper presents a numerical formulation for the analysis of unreinforced masonry walls under shear–compression fracture. To achieve this, the formulation of Attard and Tin-Loi [Attard MM, Tin-Loi F. Numerical simulation of quasibrittle fracture in concrete. Engineering Fracture Mechanics 2005;72:387–411] used for the simulation of fracture in concrete has been extended to model unreinforced masonry and enhanced by including a compression cap in the failure surface. The finite element formulation is based on a triangular unit, constructed from constant strain triangles, with nodes along its sides but not at the vertex or the center of the unit. Fracture is modeled through a constitutive softening-fracture law at the boundary nodes. The constitutive law is a single branch softening law. The material within the triangular unit remains linear elastic. Triangular units are grouped into rectangular zones which mimic brick units and mortar joints. The path-dependent softening behaviour is solved using a linear complementarity problem (LCP) formulation, in non-holonomic rate form within a quasi-prescribed displacement approach. The inelastic failure surface is modeled using a Mohr–Coulomb failure surface with a tension cut-off and a linear compression cap. The formulation is verified by comparing the results with available experimental and numerical results on shear walls under shear compression loading.