The thesis presents a novel computational method for analysing the static and dynamic behaviour of a multi-damaged beam using local and non-local elasticity theories. Most of the lumped damage beam models proposed to date are based on slender beam theory in classical (local) elasticity and are limited by inaccuracies caused by the implicit assumption of the Euler-Bernoulli beam model and by the spring model itself, which simplifies the real beam behaviour around the crack. In addition, size effects and material heterogeneity cannot be taken into account using the classical elasticity theory due to the absence of any microstructural parameter. The proposed work is based on the inhomogeneous Euler-Bernoulli beam theory in which a Dirac's delta function is added to the bending flexibility at the position of each crack: that is, the severer the damage, the larger is the resulting impulsive term. The crack is assumed to be always open, resulting in a linear system (i.e. nonlinear phenomena associated with breathing cracks are not considered). In order to provide an accurate representation of the structure's behaviour, a new multi-cracked beam element including shear effects and rotatory inertia is developed using the flexibility approach for the concentrated damage. The resulting stiffness matrix and load vector terms are evaluated by the unit-displacement method, employing the closed-form solutions for the multi-cracked beam problem. The same deformed shapes are used to derive the consistent mass matrix, also including the rotatory inertia terms. The two-node multi-damaged beam model has been validated through comparison of the results of static and dynamic analyses for two numerical examples against those provided by a commercial finite element code. The proposed model is shown to improve the computational efficiency as well as the accuracy, thanks to the inclusion of both shear deformations and rotatory inertia. The inaccuracy of the spring model, where for example for a rotational spring a finite jump appears on the rotations' profile, has been tackled by the enrichment of the elastic constitutive law with higher order stress and strain gradients. In particular, a new phenomenological approach based upon a convenient form of non-local elasticity beam theory has been presented. This hybrid non-local beam model is able to take into account the distortion on the stress/strain field around the crack as well as to include the microstructure of the material, without introducing any additional crack related parameters. The Laplace's transform method applied to the differential equation of the problem allowed deriving the static closed-form solution for the multi-cracked Euler-Bernoulli beams with hybrid non-local elasticity. The dynamic analysis has been performed using a new computational meshless method, where the equation of motions are discretised by a Galerkin-type approximation, with convenient shape functions able to ensure the same grade of approximation as the beam element for the classical elasticity. The importance of the inclusion of microstructural parameters is addressed and their effects are quantified also in comparison with those obtained using the classical elasticity theory.

This research investigated the behavior of nonseismically detailed reinforced concrete exterior beam-column joints subjected to bidirectional lateral cyclic loading using nonlinear finite element analysis (NLFEA). Beam-column joints constitute a critical component in the load path of reinforced concrete buildings due to their fundamental role in integrating the overall structural system. Earthquake reconnaissance reports reveal that failure of joints has contributed to partial or complete collapse of reinforced concrete buildings designed without consideration for large lateral loads, resulting in significant economic impact and loss of life. Such infrastructure exists throughout seismically active regions worldwide, and the large-scale risk associated with such deficiencies is not fully known. Computational strategies provide a useful complement to the existing experimental literature on joint behavior and are needed to more fully characterize the failure processes in seismically deficient beam-column joints subjected to realistic failure conditions. Prior to this study, vulnerable reinforced concrete corner beam-column joints including the slab had not been analyzed using nonlinear finite element analysis and compared with experimental results. The first part of this research focused on identification and validation of a constitutive modeling strategy capable of simulating the behaviors known to dominate failure of beam-column joints under cyclic lateral load using NLFEA. This prototype model was formulated by combining a rotating smeared crack concrete constitutive model with a reinforcing bar plasticity model and nonlinear bond-slip formulation. This model was systematically validated against experimental data, and parametric studies were conducted to determine the sensitivity of the response to various material properties. The prototype model was then used to simulate the cyclic response of four seismically deficient beam-column joints which had been previously evaluated experimentally. The simulated joints included: a one-way exterior joint, a two-way beam-column exterior corner joint, and a series of two-way beam-column-slab exterior corner joints with varying degrees of seismic vulnerability. The two-way corner joint specimens were evaluated under simultaneous cyclic bidirectional lateral and cyclic column axial loading. For each specimen, the ability of the prototype model to capture the strength, stiffness degradation, energy dissipation, joint shear strength, and progressive failure mechanisms (e.g. cracking) was demonstrated.

This thesis presents the development of a new multiscale stochastic fracture mechanics modelling framework informed by in-situ X-ray Computed Tomography (X-ray CT) tests, which can be used to enhance the quality of new designs and prognosis practices for fibre reinforced composites. To reduce the empiricism and conservatism of existing methods, this PhD research systematically has tackled several challenging tasks including: (i) extension of the cohesive interface crack model to multi-phase composites in both 2D and 3D, (ii) development of a new in-house loading rig to support in-situ X-ray CT tests, (iii) reconstruction of low phase-contrast X-ray CT datasets of carbon fibre composites, (iv) integration of X-ray CT image-based models into detailed crack propagation FE modelling and (v) validation of a partially informed multiscale stochastic modelling method by direct comparison with in-situ X-ray CT tensile test results.

The diploma thesis is focused on the evaluation of mechanical fracture parameters of concrete after exposure to high temperatures. In the introductory theoretical part general principles of fracture mechanics with the concentration on a linear elastic fracture mechanics and non-linear fracture models for the concrete are summarized. The meaning of the three-point bending fracture test used for determination of fracture parameters is also explained. Further the influence of high temperatures on the partial components of concrete and general modeling of temperature loading is described. The practical part is concerned with the evaluation of fire experiments on the concrete panels including numerical simulations using GiD and ATENA software. The evaluation of data obtained from the three-point bending test carried out on specimens with initial stress concentrator taken from concrete panels is a main part of the diploma thesis. The values of modulus of elasticity, effective fracture toughness, work of fracture and fracture energy are determined from the measured F–d and F–CMOD diagrams after their proper corrections in the GTDiPS application. The evaluation of the selected mechanical fracture parameters was performed by StiCrack software using effective crack model and work of fracture method and DKFM_BUT software using the double-K fracture model. Finally, the attention is paid to the analysis of the obtained data.