Masonry is one of the most commonly used construction materials for residential buildings and historic buildings around the world. Some of these buildings are located at seismic zones, while unreinforced masonry structures are vulnerable to seismic loads. To assess the existing masonry buildings and to design new masonry structures, nonlinear seismic simulations are conducted with macro modelling or micro modelling approach. The macro modelling approach, which smears out the details of the bricks and joints as a homogenous material, can efficiently and robustly model complete masonry structures. A commonly used orthotropic constitutive model is the Engineering Masonry Model of the DIANA FEA, which is based on the Total Strain Method that eliminates the mapping-back process in conventional elastoplastic constitutive models. The micro modelling approach, which explicitly models the bricks and joints, can better represent the mechanical behaviours of masonry. However, most of the constitutive models used in micro modelling are based on elastoplasticity that usually causes numerical difficulties due to its mapping-back process. The lack of a robust constitutive model has severely hindered the application of this accurate analysis approach.

So, this thesis proposes a sub-increment based iterative constitutive model for interface elements, based on Multi-surface Plasticity Criterion. This model aims to enhance the robustness and accuracy of the constitutive model used for micro modelling. It eliminates the conventional mapping-back process in elastoplastic constitutive models by introducing the ideas of sequential uni-axial loading algorithm and an extra damage iterative calculation algorithm. These algorithms are robust even when the stress state is at the corners of the yield surface. The model also introduces the concept of sub-increments to consider the path dependency in plastic process. All the formulations of this constitutive model are derived based on a simple mechanical model. Formulas and examples are provided for obtaining the input parameters from material tests. The proposed constitutive model is tested on a single integration point level and found to be stable and reliable. It is further applied on the component level, by modelling three masonry walls of different dimensions and boundary conditions, under cyclic loading. For the verification of these wall models, the numerical results are compared with the experimental results in terms of force-displacement curve and crack pattern. Finally, the thesis presents a brief study on parameter sensitivity to provide guidelines for the level of accuracy needed for each input parameter, in order to get satisfactory numerical results.

The constitutive model is found to be robust for all the wall analyses conducted, without encountering divergence. The comparison between numerical results and experimental results shows that this constitutive model can cover the majority of shear and flexural failure mechanisms and mimic the crack patterns well. It is capable of modelling shear failure with high accuracy. It can also model flexural failure well with a few parameters calibrated. The fact that the model is little sensitive to parameters that are hard to be measured from experiments, such as tensile strength and tensile fracture energy, ensures its feasibility in engineering practices.