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Although the mechanical behaviour of particle-reinforced and fibre-reinforced composites have been studied extensively in infinitesimal deformation regime, their properties under finite deformation are still not well understood due to the complex interaction mechanisms between matrix and reinforcement, the intrinsic material and geometry nonlinearities. In this work, theoretical analysis, numerical simulation, and experimental data in the literature are employed to investigate the mechanical properties of composites with reinforcement in finite deformation. First, a three-dimensional Representative Volume Element (RVE) is developed for neo-Hookean composite, in which the incompressible neo-Hookean matrix is reinforced with spherical neo-Hookean particles. Four types of finite deformation (i.e., uniaxial tension/compression, simple shear and general biaxial deformation) are simulated using the RVE models with periodic boundary conditions enforced. The simulation results show that the overall mechanical responses of the incompressible particle-reinforced neo-Hookean composite (IPRNC) can be well predicted by another simple incompressible neo-Hookean model. The results also indicate that the effective shear modulus of IPRNC with different particle volume fraction and different particle/matrix stiffness ratio can be well predicted by the classical linear elastic estimation. In the second half of the study, the significance of the fibre-matrix interaction in the Human Annulus Fibrosus (HAF) is identified and analysed in detail. Based on the experimental results in the literature it is shown that the mechanical behaviour of the matrix can be well simulated by the incompressible neo-Hookean type model, but the effective stiffness of the matrix depends on fibre stretch ratio, which can only be explained by fibre-matrix interaction. Furthermore, it is found that this interaction takes place anisotropically between the matrix and the fibres distributed in different proportions in different directions. The dependence of the tangent stiffness of the matrix on the first invariant of the deformation tensor can also be explained by this fibre orientation dispersion.

Cutting produces offcuts and chips in many different ways. One such process is where the chip is formed along a plane of shear inclined from the tool tip to the workpiece surface. This shear plane cutting process, found when cutting many different materials, comprises friction, plasticity and material separation. The importance of including material separation in the analysis is the main focus of this research, which involves the study of chip formation by cutting PMMA and Nylon 66 and wood.

Electronic Speckle Pattern Shearing Interferometry (ESPSI) or shearography has successfully been used in NDT for slope (δw/δx and/or δw/δy) measurement while strain measurement (δu/δx, δv/δy, δu/δy and δv/δx) is still under investigation This method is well accepted in industrial applications especially in the aerospace industry. Demand of this method is increasing due to complexity of the test materials and objects. ESPSI has successfully performed in NOT only for qualitative measurement whilst quantitative measurement is the current aim of many manufacturers. Industrial use of such equipment is being completed without considering the errors arising from numerous sources, including wavefront divergence. The majority of commercial systems are operated with diverging object illumination wavefronts without considering the curvature of the object illumination wavefront or the object geometry, when calculating the interferometer fringe function and quantifying data. This thesis reports the novel approach in quantified maximum phase change difference analysis for derivative out-of-plane (OOP) and in-plane (IP) cases that propagate from the divergent illumination wavefront compared to collimated illumination.

Most engineering components contain defects (e. g. cavities and cracks) which are usually generated during the manufacture process. During the service life of the component it is possible that the defects could grow leading to ultimate failure of the component. For safety critical engineering components, such as those used in nuclear power plant systems, rail track systems and aerospace systems, ultimate failure is not permitted. To eliminate failure, the structural integrity of the component is assessed using knowledge of both the applied and residual stress distributions present. The applied stress distributions are calculated, whereas the residual stress distributions are measured using methods like the deep-hole drilling technique. The deep-hole drilling residual stress measurement technique was investigated to increase its accuracy and reliability in measuring the residual stress distributions present within components. It is a semi-invasive technique that involves drilling a small hole through the component and then the accurate diameter measurement thereof. A cylinder of material containing the hole is then extracted from the component causing the hole to deform due to the relaxation of the residual stresses present. The hole diameter is then re-measured and the change is used to determine the pre-existent residual stress distribution. The applicability of the technique was extended through modifications made to the machining processes, to include both thicker and thinner components. The accuracy of the measurements recorded and analysis thereof were improved. A portable machine was made to carry out "on-site" deep-hole drilling residual stress measurements on large components. Calibration experiments were carried out on components containing various known stress distributions to test the accuracy and modifications of the technique, and its applicability to different materials. Finally, an extensive set of residual stress measurements were undertaken on different components varying in geometry and material composition to test the accuracy and reliability of the technique in comparison with alternative measurement methods.

The efficiency of a structure defines the relationship between its performance and cost. Studies of structural efficiency will inevitably lead to improved structural performance and/or reduced material consumption. There are various routes to achieve more efficient structures, and the use of mechanics/structural concepts provides one important option. These concepts are valid for a broad range of structures, easy to understand and play a decisive role in a conceptual or scheme design stage which is the most influential stage for determining structural efficiency. However, there are few systematic studies of structural efficiency from the perspective of mechanics concepts. This provides the rationale for exploring mechanics concepts to improve the efficiency of structures. Three effective concepts are used as a basis for this study, that more direct force paths, smaller internal forces and more uniform force/stress distribution lead to a stiffer or more efficient structure. These concepts can only be realized in particular types of structure through taking appropriate measures. Therefore, this thesis aims to improve structural efficiency by making good use of some existing measures, developing new measures, providing a theoretical basis to some effective measures and abstracting general principles from some available measures based on the three concepts. The following items are investigated in this thesis: 1. For two existing approaches searching for efficient structural forms, the intuitive use and mathematical realisation (evolutionary structural optimization (ESO)) of structural concepts, their complementary characters are first identified which inspire a comparative study of the solutions. Through this study, the efficient profiles of a mid-span loaded thick beam and effective bracing arrangements for laterally braced frames are revealed; governing concepts affecting structural efficiency in particular conditions are discussed; and some design measures for designing efficient structural forms in the two groups of cases are presented. 2. As new measures, design criteria for effective bracing systems in simple and tall frames are developed, based on the concepts of direct force paths and small internal forces. The criteria are shown to be effective as a two-stage design procedure, with the arrangement of braced panels followed by that of bracing member orientation. 3. A theoretical study of an existing beam stiffening measure using external tendons is conducted, focusing on the stiffness and natural frequencies of a stiffened beam. It provides quantitative estimation of the stiffening effect and theoretical evaluation of the governing factors and optimal profile for designing the profiled tendons. 4. The effective measures leading to the high efficiency of the Raleigh Arena are identified and studied. The efficiency of the Arena is evaluated quantitatively using numerical methods. The concept of smaller internal forces can be abstracted from one physical measure used in the Arena.

In the deformation of layered materials such as geological strata, or stacks of paper, mechanical properties compete with the geometry of layering. Smooth, rounded corners lead to voids between layers, while close packing leads to geometrically induced curvature singularities. When creation of voids is penalized by external pressure, the system trades off these competing effects, leading to various accommodating formations. Three two dimensional energy based nonlinear models are presented to describe the formation of voids at areas of intense geological folding. For each model the layers are assumed to be flexible elastic beams under hard unilateral contact constraint; which are solved as quasi-static obstacle problems with a free boundary. In each case an application of Kuhn-Tucker theory leads to representation as a nonlinear fourth order differential equation. Firstly a single layered model for voiding is presented. An elastic layer is forced into a V-shaped singularity by a uniform overburden pressure, where the fourth order free boundary problem is shown to have a unique, convex, symmetric solution. Drawing parallels with the Kuhn-Tucker theory, virtual work and ideas of duality, the physical significance of this differential equation is emphasised. Finally, appropriate scaling of either the potential energy or the differential equation shows the solutions scale to a single parametric group, for which the size of the void scales inversely with the ratio of overburden pressure to bending stiffness of the layer. Common to structural geology, one or several especially thick layers can dominate the deformation process. As a result, the remaining weak layers must accommodate into the geometry imposed by these competent layers. The second model, extends the first by introducing a plastic hinge to replicate the geometry imposed by the competent layer, and also axial springs to resist the slip over the limbs. The equilibrium equations for the system are investigated using the mathematical techniques developed for the first model. Under rigid loading the system may snap from an initially flat state to a convex voiding solution, as seen in the first model. However, if resistance to slip is high, the slightest imperfection causes the system to jump to a convoluted up-buckled solution, following a de-stiffened path to a point of self contact. These solutions have similarities with the delamination of carbon fibre composites. Finally, we extend the two single layered models to a simple multilayered model, which describes the periodic formation of voids in a chevron fold. The model shows that in the limit of high overburden pressures solutions form voids every layer, producing straight limbs punctured by sharp corners. This analysis shows good agreement when compared with recent experiments. This work provides the basis for future work on the buckling of thin multilayer assemblies in which voids may develop, and emphasizes the importance of the intricate nonlinear constraints of layers fitting together in multilayered folds.

Σκοπός της παρούσας διδακτορικής διατριβής είναι η ανάπτυξη αριθμητικής μεθόδου, η οποία επιλύει προβλήματα δισδιάστατης στατικής ελαστικότητας, καθώς και δυναμικής ελαστικότητας στο πεδίο των συχνοτήτων και στο πεδίο του χρόνου. Το κύριο χαρακτηριστικό της είναι ότι η προσέγγιση του άγνωστου πεδίου γίνεται με την τοποθέτηση σημείων και όχι με τη χρήση κάποιου πλέγματος όπως γίνεται στις μέχρι τώρα κλασικές μεθοδολογίες των πεπερασμένων ή συνοριακών στοιχείων. Μέρος της παρούσας διατριβής αποτελεί και η ανάπτυξη προγράμματος ηλεκτρονικού υπολογιστή, ο οποίος υποστηρίζει πλήρως τα όσα αναφέρονται στην παρούσα εργασία. Η παρούσα διατριβή αποτελείται από δύο ενότητες. Στην πρώτη ενότητα, η οποία περιλαμβάνει τα πρώτα τρία κεφάλαια, παρατίθεται το θεωρητικό υπόβαθρο της μεθοδολογίας. Στη δεύτερη ενότητα περιγράφονται διάφορες τεχνικές λεπτομέρειες, όπως ολοκληρώσεις και προσέγγιση πεδίου και δίνονται αρκετά παραδείγματα, τα οποία πιστοποιούν την ακρίβεια και την αξιοπιστία της. / -

Foreign object damage (FOD) refers to the damage that generally takes place in aero engine fans and compressor blades, due to the ingestion of hard particles/debris during aeroplane take-off, taxiing, or landing. Such damage can reduce the fatigue life expectancy of the turbine engine components by 50%. Residual stresses and small microcracks induced by the high speed FOD impacts are two root causes that result in premature failure of these components. One way to mitigate the FOD related fatigue failure is to induce deep compressive residual stress into the surface. Among the available techniques that can induce such compressive residual stress, laser shock peening (LSP) has been found to be beneficial in improving the fatigue strength. In this study aerofoil-shaped Ti-6Al-4V leading edge specimens were laser shock peened. Subsequently, FOD was introduced onto the leading edge specimen through ballistic impacts of a cube edge at angles of 0° and 45° to the leading edge. The effect of foreign object damage (FOD) on the pre-existing compressive residual stress field associated with the laser shock peening (LSP), and its change upon solely low cycle fatigue (LCF) as well as combined low and high cycle fatigue cycling has been studied. The residual stress distribution and their redistribution upon fatigue cycling were mapped around the FOD notch, using synchrotron X-ray radiation and the contour method. The results suggest that under both impact angles, the FOD event superimposed a significant additional residual stress on top of the pre-existing stress associated with the LSP process. It has been observed that the FOD notch created by 45° impact was asymmetric in shape, and had differential notch depth between the entry and exit side. However, FOD damage that is created at 0° impact appeared as a sharp V notch. A higher amount of residual stresses were produced under 0° impact condition than at 45°. It has been found even though the FOD induced residual stresses relax, residual stresses due to LSP treatment remain highly stable even in the worst condition where a 7 mm long crack was grown from a 45° notch. The plastic zone sizes ahead of a crack tip was estimated for both 0° and 45° FOD impact, and the fatigue crack growth rates are predicted utilizing the measured residual stress distribution.