Masonry is one of the most common building materials globally due to its ease of construction, price, durability and fire resistance. Its heterogeneity and orthotropic nature make its mechanical behaviour rather complex, highlighting the importance of an appropriate constitutive model to describe such behaviour accurately. In literature, most of the existing constitutive models for masonry fall in one of the two following categories: macro-models or micro-models. The micro-models (also called block-based models), which explicitly describe masonry's geometrical and material heterogeneities, exhibit higher accuracy but require higher numerical efforts when simulating masonry's mechanical behaviour. The macro-models (also called continuum models), which model masonry as homogeneous material and smear out the damage over the continua, are less accurate but offer a good compromise between accuracy and numerical efficiency. They are therefore used more often to simulate masonry structures. However, most of the macro-models are not capturing well the damage localization occurring along the mortar joints and the energy dissipation in the bricks and mortars. To increase the applicability of continuum models, the components' damage localization and energy dissipation should be improved. This thesis presents a homogenized constitutive model for applications on masonry structures under in-plane loading. The developed homogenized material model for masonry includes the description of shearing, tensile cracking, crushing and splitting. Inspired by the micro-mechanical models of Zucchini and Lourenço, four models were developed in this thesis to describe the different types of in-plane failure of masonry, naming: tensile failure of bed joints, horizontal shear sliding of bed joints, tensile cracking of unit, diagonal tensile cracking failure, masonry crushing failure. The first model is derived for the masonry’s pure shear behaviour, where the shear sliding failure is introduced. The second one is derived for the horizontal tensile behaviour, where the vertical tensile cracking of brick units and the vertical joints is proposed. The third one is derived for the vertical compression behaviour, where masonry crushing failure is adopted. The fourth one is coupling the failure mechanisms described in the previous three models with a novel algorithm. Additionally, the diagonal tension cracking failure and the horizontal tensile cracking of horizontal joints are incorporated in the fourth and final material model. To derive these models, first, a representative volume element (RVE) was selected for running bond wall, where the bricks are staggered by half-length of brick from the adjoining courses above and below. Each RVE consists of two-quarters of bricks connected through a bed joint, and each one is connected to a head joint on one side. For each of the models, the active internal stresses of each component (brick, bed, head or cross joint) are calculated through the compatibility and equilibrium equations resulting from the assumed deformed mechanisms. Different damage state variables are introduced for every component in the damage model, where exponential softening is assumed for tension and shear. Additionally, a Ducker-Prager yield criterion with bi-parabolic hardening is used in combination with an explicit Euler-forward algorithm to describe the elastoplastic behaviour of the material in compression. As a result, the material model’s constitutive law is obtained with the homogenization procedures after coupling the damage and plastic model together by a specific algorithm originally introduced by Zucchini and Lourenço. The constitutive equations for model 1 (shear), model 2 (tension), model 3 (compression) and model 4 (coupled) were coded successfully in MATLAB. The components’ shearing, tensile cracking, crushing and splitting failures are correctly modelled analytically with an algorithm, which can be applied to simplify the micro-mechanical model. Besides, constitutive laws of models 1 and 2 were also implemented successfully in the finite element software DIANA version 10.4 (check). The ability of the model to capture the failure of the components in shear, tensile cracking or crushing was examined through simple analytical applications. Moreover, the model was compared against experimental results from tests performed on masonry wallets under compressive loading; the model was able to predict the strength of the specimens satisfactorily. Therefore, this alternative constitutive material model can adequately simulate masonry’s behaviours with a simpler algorithm than the previous model. Meanwhile, the component’s elastic and elastoplastic behaviours can be simulated in more detail in this model, as the case that the horizontal joint is first damaged in shear and compressive splitting effects are additionally included.

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.