Crack propagation analysis in masonry structures via an inter-element cohesive fracture approach: Assessment of mesh dependency issues

Inter-element cohesive methodologies have proved to be very effective to simulate complex cracking phenomena in quasi-brittle materials, by virtue of their capability of naturally handling multiple crack nucleation and propagation along unknown paths, also including crack bifurcation and coalescence. Nevertheless, in several computational implementations, such methodologies suffer from a certain mesh bias, since crack propagation is restricted to occur along inter-element mesh boundaries. Besides, the resulting structural response is inevitably affected by the additional compliance provided by the embedded cohesive elements with finite stiffness even prior to the crack onset. In this work, the diffuse inter-element cohesive method has been applied to masonry structures, focusing the attention on the role of related mesh dependency issues. In particular, the aim of this work is twofold. First, a novel calibration approach of the initial cohesive stiffness is developed to reduce the aforementioned artificial compliance effect. Second, an effective strategy is proposed to avoid the occurrence of multiple solutions, which are typical of diffuse inter-element cohesive approaches, especially in structured meshes. To assess the validity of the proposed method, numerical simulations of the failure behavior of simple masonry specimens are performed. The results show that a rational calibration of the cohesive properties (i.e., stiffness and strength) of diffuse embedded interfaces is useful to ensure numerical stability and accuracy, in terms of both load-bearing capacity and related crack pattern.