Simplified homogenization technique for nonlinear finite element analysis of in-plane loaded masonry walls

The present investigation focuses on the nonlinear modelling of masonry walls under in-plane loading. To conduct this macro-scale study, a homogenization technique is applied to derive the equivalent secant moduli according to damage and friction sliding at the micro scale level for both bed mortar joint and brick material constituents. In the homogenization process the representative unit cell of masonry panel with a regular arrangement is first defined. Then a simplified kinematical model is proposed to describe the behaviour of the homogenized unit-cell under combined axial and shear stresses. This is based on the cohesive model for pure mode I and II and by allowing for the Coulomb's friction law for bed joint and the scalar damage model is adopted for the brick material. In the first stage, the proposed homogenization technique is verified for various unit cell constituents at micro-scale level. In the second step, this homogenization procedure was incorporated into proposed in-house finite elements software. To achieve this end, a new beam finite element is formulated in the context of the fibre higher order shear deformation theory HSDT. Using the proposed finite elements model, a numerical investigation is conducted to check the validity of the proposed model against the available experimental and numerical investigations. This allowed for the study of the effect of the applied compressive load on the lateral ultimate load.