A study of mechanical and capillary bifurcation phenomena in soft elastic materials

Stress-induced pattern formations in soft elastic materials are bifurcation phenomena which can be localized or periodic. Certain localized pattern formations such as necking or bulging are associated with zero wavenumber, whereas periodic pattern formations such as wrinkling or buckling are associated with a strictly positive wavenumber. Whilst the near-critical behaviour of the periodic case is well understood, studies of the localized case have only recently gathered momentum, and are conceptually more challenging to undertake. Despite this, a remarkable amount of analytical progress can be made. We will highlight this generally underappreciated fact by studying theoretically the complete bifurcation behaviour of localized patterns, as well as the competition from periodic patterns, in elastic materials under various effects. Firstly, the bifurcation behaviour of soft incompressible hollow tubes under elasto-capillary effects is studied. Analytical bifurcation conditions for localized pattern formation are initially derived using established results from a prototypical problem. A linear bifurcation analysis then shows that an axi-symmetric zero wavenumber bifurcation mode is favoured over periodic modes for a range of boundary conditions and loading scenarios. A weakly non-linear analysis provides an explicit connection between this zero wavenumber mode and localized necking or bulging, and a phase-separation-like evolution of these localized patterns into a final Maxwell state is described analytically. The effect of material compressibility on localized pattern formation in soft cylinders is also studied analytically, and comparisons with recently published numerical simulation results are made. We then consider the formation of a self-contacting crease on the free surface of a compressed elastic half-space. This is a highly unique localized pattern since its inception is an inherently non-linear bifurcation phenomenon. Therefore, unlike localized bulging or necking, it is undetectable through a linear analysis. We derive a new analytical bifurcation condition for creasing by reformulating the analysis of a recent ground-breaking study

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Waves and Ocean Structures

Ocean Structures subjected to actions of ocean waves require safety inspection as they protect human environment and everyday lives. Increasing uses of ocean environment have brought active research activities continuously. The newly developed technology of ocean energy even pushed the related needs forward one more step. This Special Issue focuses on Analysis of Interactions between wave structures and ocean waves. Although ocean structures may cover various practical and/or conceptual types, we hope in the years to come, the state-of-the-art applications in wave and structure interactions and/or progress review and future developments could be included. There are fifteen papers published in the Special issue. A brief description includes: Lee et al. [1] presented a concept of a water column type wave power converter. Li et al. [2] considered submerged breakwaters. Lin et al. [3] studied an ocean current turbine system. Thiagarajan and Moreno [4] investigated oscillating heave plates in wind turbines. Chiang et al. [5] proposed an actuator disk model. Tseng et al. [6] investigated Bragg reflections of periodic surface-piercing submerged breakwaters. Lee et al. [7] analyzed caisson structures with a wave power conversion system installed. Yeh et al. [8] reported motion reduction in offshore wind turbines. Wu and Hsiao [9] considered submerged slotted barriers. Tang et al. [10] studied floating platforms with fishnets. Chen et al. [11] calculated mooring drags of underwater floating structures with moorings. Jeong et al. [12] estimated the motion performance of light buoys using ecofriendly and lightweight materials. Zhang et al. [13] considered vibrations of deep-sea risers. On the other hand, Shugan et al. [14] studied the effects of plastic coating on sea surfaces

An Integrated Nonlinear Wind-Waves Model for Offshore Wind Turbines

This thesis presents a numerical model capable of simulating offshore wind turbines exposed to extreme loading conditions. External condition-based extreme responses are reproduced by coupling a fully nonlinear wave kinematic solver with a hydro-aero-elastic simulator. First, a two-dimensional fully nonlinear wave simulator is developed. The transient nonlinear free surface problem is formulated assuming the potential theory and a high-order boundary element method is implemented to discretize Laplace's equation. For temporal evolution a second-order Taylor series expansion is used. The code, after validation with experimental data, is successfully adopted to simulate overturning plunging breakers which give rise to dangerous impact loads when they break against wind turbine substructures. Emphasis is then placed on the random nature of the waves. Indeed, through a domain decomposition technique a global simulation framework embedding the numerical wave simulator into a more general stochastic environment is developed. The proposed model is meant as a contribution to meet the more and more pressing demand for research in the offshore wind energy sector as it permits taking into account dangerous effects on the structural response so as to increase the global structural safety level

Dynamic energy dissipation using nanostructures: mechanisms and applications

The emerging subject of mechanical impact protection at nanoscale where solids, fluids interact closely, has raised many multi-disciplinary and challenging questions which cannot be answered by the analogy from their macroscopic counterparts. A series of counterintuitive phenomena have been observed without further profound theoretical explanations. It is pretty straightforward to take advantage of these novel properties for fascinating applications which cannot be achieved by traditional materials and structures. Among various exciting areas, one of the most promising and ever expanding topics is the impact protection at nanoscale. Primarily inspired by the excellent mechanical properties of carbon nanotube (CNT), a water-filled CNT system for impact protection is designed. The nanoconfined water molecules enhance the stiffness of the tube and also help to stabilize the tube such that the buckling force and the post-buckling plateau is higher than empty CNTs, indicating a much higher energy dissipation performance. Also, the energy dissipation performance is dependent on the aspect ratio which is similar in its bulk counterpart. Additional support may come from adjacent tubes in CNT bundle and forests and the actual energy dissipation per unit volume/mass is improved. Unlike the tube or beam shape, once the single layer graphene is rolled into a spherical shell, it becomes buckyball whose mechanical properties are seldom studied. Thus, firstly, the quasi-static and dynamic behavior of buckyball is investigated based on MD simulation. Buckyball may be categorized according to the mechanical behavior. The force-displacement curve obey the continuum shell model prediction perfectly except for the slight difference in coefficient change due to the size effect. Interestingly, it is discovered that larger buckyball cannot recover to its original shape after unloading while the smaller buckyball can. Stronger van der Waals interaction between the buckled layer and the bottom layer may be the responsible reason for the non-recovery phenomenon. The buckled shape should have higher strain energy such that more mechanical energy is dissipated. Motivated by the novel behavior of buckyball, the various stacking forms of buckyball are investigated. By analogy for the 1D granular energy dissipation system, a 1D long chain buckyball system is designed and studied. With relatively small elastic deformations of C60 buckyballs during impact, a modified Hertz contact model is proposed, with critical parameters calibrated via MD simulations for given impact loading conditions. The major energy dissipation mechanism for the buckyball chain is the wave reflection among the deformation layers, covalent potential energy, van der Waals interactions as well as the atomistic kinetic energy. For nonrecovery buckyballs such as C720, energy mitigation effect is more obvious. Over 99% and 90% of impact energy for C720 and C60 chain systems could be mitigated under particular impact conditions. Moreover, protective system based on short 1D vertical and horizontal alignments and various pseudo 3D stacking forms with different packing densities are also studied. It is found that stacking form with higher occupation density yields higher energy absorption and proves the available buckyball in bulk is ready for impact protection. In addition, to quantify the material behavior, prove the recently suggested new theories and discover new phenomenon, desktop experiments serves as an important part of this thesis research. The governing factors, i.e. pre-treatment temperatures, solid-to-liquid mass ratio, particle size and electrolyte concentration are parametrically studied. Experiments show that the optimum processing pretreatment temperature is about 1000 degree; with higher zeolite mass ratio. Also, the dynamic behavior of zeolite beta/water system is investigated and the system has a better dynamic performance than quasi-static since the infiltration pressure increases due to the water molecule inertia effect. To conclude, impact dynamics and energy dissipation/mitigation at nanoscale is a lasting topic in mechanics related research area whose knowledge is highly desire in engineering application with the advancement of material science, physics and chemistry

Localized buckling of an elastic strut in a visco-elastic medium

Certain types of long, axially compressed structures have the potential to buckle locally in one or more regions rather than uniformly along their length. Here, the potential for localized buckle patterns in an elastic layer embedded in a visco-elastic medium is investigated using a strut-on-foundation model. Applications of this model include the growth of geological folds and other time-dependent instability processes. The model consists of an elastic strut of uniform flexural stiffness supported by a Winkler-type foundation made up of discrete Maxwell elements. Mathematically, this model corresponds to a nonlinear partial differential equation which is fourth­order in space and first-order in time. The nature of the buckling process is charac­terized by an initial period of elastic deformation followed by an evolutionary phase in which both elasticity and viscosity have a role to play. Two different formulations are studied: the first combines linear strut theory with a nonlinear foundation and is valid for small, but finite, deflections; the other incorporates the exact expression for curvature of the strut resulting in geometrical nonlinearities and is capable of modelling large deflections. The evolution of non-periodic buckle patterns in each system is examined under the constraint of controlled end displacement. Two independent methods are used to approximate the solution of the governing equations. Modal solutions, based on the method of weighted residuals, complement accurate numerical solutions obtained with a boundary-value solver. In either case, the results suggest that for the perfect system, localized solutions follow naturally from the inclusion of nonlinear elasticity with softening characteristics. Emphasis throughout is on the qualitative features displayed by the phenomenon of localization rather than specific applications. Nevertheless, the ideas and results are a step towards accounting for the rich variety of deformed shapes exhibited by nature.Open Acces

Viscoelasticity

This book contains a wealth of useful information on current research on viscoelasticity. By covering a broad variety of rheology, non-Newtonian fluid mechanics and viscoelasticity-related topics, this book is addressed to a wide spectrum of academic and applied researchers and scientists but it could also prove useful to industry specialists. The subject areas include, theory, simulations, biological materials and food products among others