Enriched plane state formulation for nonlinear homogenization of in-plane masonry wall

The present study deals with the determination of the nonlinear response of the masonry regarded as a regular, i.e. periodic, composite material made of bricks and mortar. A homogenization procedure is applied deriving the masonry overall mechanical response on the basis of the study of a single unit cell. An enriched plane state kinematic model including the effect of the transversal strains of the masonry is presented. This is a simplified form of the full three-dimensional approach. Different cohesive constitutive models are introduced for the brick and mortar; in particular, the frictional effect, playing an important role in the masonry response, is accounted for in the mortar joints. Two main issues are addressed: (a) different structural models are considered at macro- and micro-scale: the macro-model is formulated in the two-dimensional plane state context, while the enriched plane state kinematic approach is adopted at the microlevel; (b) a nonlocal integral strain technique, able to overcome the classical localization drawbacks due to the softening response of the masonry constituents, is developed for the case of periodic media. Numerical applications are presented to assess the effectiveness of the proposed modeling approach.