Interface Fracture in Masonry Composites: A Lattice Approach
The brick-mortar bond or interface is often the weakest link in the masonry composites. The localization of fracture processes at this bi-material interface plays an important role in the failure of this assemblage. These micro-level fracture processes control the nonlinear behavior of the brick-mortar interface which significantly affects the global behavior of the masonry structure at the continuum macro level. 2D Lattice-based micro-level fracture simulations which are based on Voronoi tessellation to discretize the continuum brick and mortar domains are applied to study progressive debonding of brick-mortar interfaces in unreinforced masonry composites. An energy method is subsequently employed to obtain the energy release rate of the lattice mesh as the crack propagates which is determined by considering the variation in the global stiffness matrix of the mesh with respect to crack length change. This energy release rate is inserted into the Irwin type fracture relationship for plane strain to calculate the modulus of complex stress intensity factor and its mode 1 and mode 2 values which are independent of the distance from the crack tip in the lattice. The lattice results for the energy release rate and stress intensity factors are then validated by comparing with three classic fracture mechanics problems analytical solutions of which are available in the literature. Afterwards, the 2-D plane strain lattice formulation is applied to simulate interfacial fracture properties of conventional test configurations in masonry. The computational lattice model is capable of evaluating the fracture toughness of brick-mortar interface along with other fracture properties from basic strength properties of lattice struts, which are removed by erosion upon failure. This information is employed to upscale the lattice fracture arguments onto the meso-level to quantify the fracture energy formulation of traction-separation cohesive zone models in the context of continuum finite element simulations of heterogeneous media such as masonry. The fracture energy from the lattice is also used in homogenizing a heterogeneous anisotropic masonry unit cell under direct tension using energy equivalence concept to obtain a scalar damage parameter which could be utilized to model the nonlinear behavior of a homogenized isotropic continuum finite element.