A unilateral nonlocal tensile damage model for masonry structures

In the present paper, a constitutive nonlocal damage model is proposed for the non-linear incremental finite element analysis of masonry structures. The mechanical model is based on the assumptions of linear elasticity under compression and softening behaviour under tension, described by the adoption of a unique strain-driven nonlocal damage variable. Specifically, non-locality of the integral type is introduced in order to prevent spurious strain localization. It can be noted that the unilateral nature of the model is suitable to contemplate both diffused macro-cracks induced by the tensile damage process and the stiffness recovery in the transition from tension to compression, considering the anisotropy induced by the damage process as well. This is performed by realizing a decomposition of the strain tensor in its positive and negative components, and accounting for stiffness degradation only along tensile direction. The assumption of a linear elastic behaviour in compression is motivated by the fact that the main interest of the model is represented by investigating the response of masonry structures under service loads, condition in which very low compressive states are usually predominant. Consequently, the number of constitutive parameters is more limited with respect to other models that include a damage criterion also in compression. Finally, the validation of the proposed damage model is carried out with reference to a plane problem, in order to check the capability of the model to treat damage in an anisotropic way as well as the almost null dependence of the results on the discretization.