Modeling initiation and propagation of fracture is the critical aspect of failure analysis of concrete and masonry structures. In the last decades, an increasing effort has been devoted to simulate fracture processes using a discrete approach where all inelastic phenomena are concentrated in zero thickness interface elements assuming that the surrounding continuum elements remain in the linear elastic range. In this approach, the computational failure of simulating large masonry structures benefits from this simplification. However, the gain in computational efficiency comes at the expense of losing modeling accuracy.

In this work the development and finite element implementation of an interface constitutive formulation is addressed for modeling the initiation and propagation of fracture under combined normal and shear stresses in masonry structures. In addition to the traditional failure in tension and shear, the interface material model includes a compressive cap to account for the inelastic behavior of masonry in compression (i.e. crushing failure). To integrate in time the constitutive rate equations and the evolution equations of the internal variables, a fully implicit Backward Euler method is applied together with Newton-Raphson method to solve the nonlinear system of equations in a monolithic fashion. To this end, the consistent tangent operator is evaluated at the material level for implementing the Newton-Raphson method at the element and structural level in order to obtain quadratic convergence.