The numerical treatment of nonlocal problems, which taking into account material microstructures, by means of meshless approaches is promising due to its efficiency in addressing integropartial differential equations. This thesis focuses on the investigation of meshless methods to nonlocal elasticity. Firstly, mathematical constructions of meshless shape functions are introduced and their properties are discussed. Shape functions based upon different radial basis function (RBF) approximations are implemented and solutions are compared. Interpolation errors of different meshless shape functions are examined. Secondly, the Point Collocation Method (PCM), which is a strong-form meshless method, and the Local Integral Equation Method (LIEM) that bases on the weak-form, are presented. RBF approximations are employed both in PCM and LIEM. The influences of support domains, different kinds of RBFs and free parameters are studied in PCM. While in LIEM, analytical forms of integrals, which is new in meshless method, is addressed. And, the number of straight lines that enclose the local integral domain as well as the integral radius are analyzed. Several examples are conducted to demonstrate the accuracy of PCM and LIEM. Besides, comparisons are made with Abaqus solutions. Then, PCM and LIEM are applied to nonlocal elastostatics based on the Eringen's model. Formulations of both methods are reported in the nonlocal frame. Numerical examples are presented and comparisons between solutions obtained from both methods are made, validating the accuracy and effectiveness of meshless methods for solving static nonlocal problems. Simultaneously, the influence of characteristic length and portion factors are investigated. Finally, LIEM is employed to solve nonlocal elastodynamic problems. The Laplace transform method and the time-domain technique are implemented in LIEM respectively as the time marching schemes. Numerical solutions of both approaches are compared, showing reasonable agreements. The influence of characteristic length and portion factors are investigated in nonlocal dynamic cases as well.

Solid particles tend to adhere to fluid interfaces under the action of capillary force. This adsorption process is robust and has been exploited in lots of applications from stabilisation of emulsions to micro fluidic fabrications. The resulting particle laden fluid interfaces can manifest solid-like behaviours. The modifi cation of the surface tension and the emergence of surface shear elasticity of a particle-covered drops are attributed to the particle-induced surface stress. This stress represents at the continuum level the microscopic effect of particle-particle interactions. Understanding the link between the surface stress and the particle arrangement are crucial for creating novel soft materials in the future. A challenge remains when carrying out numerical simulations of particle-laden fluid interfaces: the large separation of scales makes the direct numerical simulations extraordinary expensive. Physical features present in the system come from both the liquid meniscus on the surface of each particle and the fluid interfaces containing thousands of particles. Motivated by the need for a fast simulation method to study problems involving particle-laden fluid interface, this thesis presents a new numerical formulation named Fast Interface Particle Interaction (FIPI) that can be used to simulate a large number of solid particles absorbed on fluid interfaces at a moderate computational cost. The outstanding performance of this new method is attributed to the fact that particle-level phenomena are modelled with analytical or semi-empirical expressions while hydrodynamics and fluid interface morphology at larger scales are fully resolved. Two important studies of particle-covered drops have been carried out with FIPI. In the first one a particle-covered pendant drop is simulated. The result reveals that the FIPI can successfully capture the modulation of surface tension made by absorbed particles. Moreover, the information of anisotropic surface stress is now directly available on the fluid interfaces. This capability has not been achieved previously in both experiments and simulations. The anisotropic stress emerged on the surface of a pendant drop is caused by anisotropic arrangement of the particles on the interface which in turn is induced by stretching of the interface due to gravity. Once the surface tension of the fluid interface is reduced below zero, the Laplace pressure inside the drop becomes negative and the drop can buckle like a thin solid elastic shell under compression. In the second study, the behaviours of a particle covered spherical drop under compression have been explored. The simulation results indicate the possibilities of particle desorption as well as fluid interface buckling. The onset of desorption is highly correlated to small-scale monolayer undulations which can greatly amplify the normal forces pushing particles out of the interface. The behaviours of a particle-covered drop under compression depend on the combination of several parameters related to the properties of the particle and the surface pressure created by the monolayer.

Tissue engineering and regenerative medicine aim to develop materials that mimic some of the characteristics of the tissue they are replacing and control the growth and proliferation of cells. Despite exceptional advances in the range and quality of materials used, much remains to discover about the processes regulating interfaces between cells and their surroundings, or at cell-material interfaces. In order to study and control such interactions, scientists have produced engineered matrices aiming to mimic some of the feature of natural extra-cellular matrix (biochemistry, geometry/topography and mechanical properties). In order to pattern 2D-nanofibers on relatively large areas and throughput, allowing comprehensive biological studies, we developed a nano-fabrication technique based on the deposition of sparse mats of electrospun fibres with different diameters. These mats are used as masks to grow cell resistant polymer brushes from exposed areas. After removal of the fibres, the remaining brushes define a quasi-2D fibrous pattern onto which ECM molecules such as fibronectin can be adsorbed. Chapter 2 includes details of the techniques used to produce and characterize the fibrous nanopattern. Chapter 3 is focused on cell phenotype observed on the different nanofibres sizes. Adhesion assays showed that cell spreading, shape and polarity are regulated by the size of fibres but also the density of the nanofibres, similarly to previous observations made on circular nanopatterns. We then focused on the study of focal adhesion formation and maturations on these nanofibres and the role of key proteins involved in the regulation of the adhesion plaque: integrins and vinculin. Cells expressing different integrins were found to sense the nanoscale geometry differently. Vinculin sensing is the topic of Chapter 4. Although vinculin recruitment dynamics was affected by the nanofibrous patterns and focal adhesions arrange differently on the nanofibres, this protein does not seem to mediate nanoscale sensing. In Chapter 5, we finally focused on the role of the actin cytoskeleton as a direct sensor of nanoscale geometry. A gradual decrease in stress fibre formation was observed as the nanofibres dimensions decrease. Live imaging also demonstrated that the geometry of the extracellular environment strongly affects cytoskeleton rearrangement, stress fibres formation and disassembly. We identify the role of cytoskeleton contractility as an important sensor of the nanoscale geometry. Our study provides a deeper insight in understanding cell adhesion to the extracellular environment and the role of the matrix geometry and topography on such phenomena, but also raises questions regarding the more detailed molecular sensory elements enabling the direct sensing of nanoscale geometry through the actin cytoskeleton.

Fracture mechanics plays an important role in understanding the performance of all types of materials including Functionally Graded Materials (FGMs). Recently, FGMs have attracted the attention of various scholars and engineers around the world since its specific material properties can smoothly vary along the geometries. In this thesis, the Finite Block Method (FBM), based on a 1D differential matrix derived from the Lagrangian Interpolation Method, has been presented for the evaluation of the mechanical properties of FGMs on both static and dynamic analysis. Additionally, the coefficient differential matrix can be determined by a normalized local domain, such as a square for 2D, a cubic for 3D. By introducing the mapping technique, a complex real domain can be divided into several blocks, and each block is possible to transform from Cartesian coordinate (xyz) to normalized coordinate (ξησ) with 8 seeds for two dimensions and 20 seeds for three dimensions. With the aid of coefficient differential matrix, the differential equation is possible to convert to a series of algebraic functions. The accuracy and convergence have been approved by comparison with other numerical methods or analytical results. Besides, the stress intensity factor and T-stresses are introduced to assess the fracture characteristics of FGMs. The Crack Opening displacement is applied for the calculation of the stress intensity factor with the FBM. In addition, a singular core is adopted to combine with the blocks for the simulation of T stresses. Numerical examples are introduced to verify the accuracy of the FBM, by comparing with Finite Element Methods or analytical results. Finally, the FBM is applied for wave propagation problems in two- and three-dimensional porous mediums considering their poroelasticities. To demonstrate the accuracy of the present method, a one-dimensional analytical solution has been derived for comparison.

The ability to extract accurately the stress intensity factor and the T-Stress for fractured engineering materials is very significant in the decision-making process for in-service engineering components, mainly for their functionality and operating limit. The subject of computational fracture mechanics in engineering make this possible without resulting to expensive experimental processes. In this thesis, the Finite Block Method (FBM) has been developed for the meshless study of interface stationary crack under both static and dynamic loading in bi-materials. The finite block method based on the Lagrangian interpolation is introduced and the various mathematical constructs are examined. This includes the use of the mapping technique. In a one-dimensional and a two-dimensional case, numerical studies were performed in order to determine the interpolation error. The finite block method in both the Cartesian coordinate and the polar coordinate systems is developed to evaluate the stress intensity factors and the T-stress for interface cracks between bi-materials. Using the William's series for bi-material, an expression for approximating the stress and displacement at the interface crack tip is established. In order to capture accurately the stress intensity factors and the T-stress at the crack tip, the asymptotic expansions of the stress and displacement around the crack tip are introduced with a singular core technique. The accuracy and capability of the finite block method in evaluating interface cracks is demonstrated by several numerical assessments. In all cases, comparisons have been made with numerical solutions by using the boundary collocation method, the finite element method and the boundary element method, etc.

To support the concept of environmentally friendly materials and sustainable development, the low-carbon cementitious materials have been extensively studied to reduce amount of CO2 emission to the atmosphere. One of the efforts is to promote alternative cementitious binders by utilizing abundant alumina-silicate wastes from the industrial sectors (e.g. fly ash or furnace slag), among which “Geopolymer (GP) cement” has received most attention as it can perform a wide variety of behaviours, in addition to cost reduction and less environmental impacts. The most common geopolymer production, fly ash-based, gained some strength with very slow rate at ambient temperature, while the strength is evidently improved when cured in high (above room) temperature, e.g. over 40°C. The major challenge is to step over the limitation of heat curing process and inconvenience in practice. In this study, the testing schemes of (i) GP manufacturing in various processes, (ii) inclusion of ordinary Portland cement (OPC) in GP mixture, called GeoPC and (iii) GeoPC manufactured with dry-mixing method, have been intensively investigated through mechanical testing (Setting time, Compressive strength and Internal heat measurement) and mechanism analysis (XRD, FTIR, SEM and EDXA) in order to develop the geopolymers, achieving reasonable strength without external sources of heat curing. It is found that the proposed (dry) mixing process could have generated intensive heat liberation which was observed as a comparable factor to heat curing from any other external sources, enhancing the curing regime of the mixture. The additional calcium content in the developed GeoPC system not only resulted in an improvement of an early strength by the extra precipitation of calcium compounds (C,N-A-S-H), but also provided a latent heat from the reaction of its high potential energy compounds (e.g. OPC or alkaline activators). The developments from these approaches could lead to geopolymer production to achieve reasonable strength in ambient curing temperature known as “Self-cured geopolymer cement”, without external heat, and hence provide construction industry viable technologies of applying geopolymers in on-site and off-site construction.