VAM Applied to Dimensional Reduction of Nonlinear Multifunctional Film-fabric Laminates

This work aims at asymptotically accurate dimensional reduction of non-linear multi-functional film-fabric laminates having specific application in design of envelopes for High Altitude Airships (HAA). The film-fabric laminate for airship envelope consists of a woven fabric core coated with thin films on each face. These films provide UV protection and Helium leakage prevention, while the core provides required structural strength. This problem is both geometrically and materially non-linear. To incorporate the geometric non-linearity, generalized warping functions are used and finite deformations are allowed. The material non-linearity is handled by using hyper-elastic material models for each layer. The development begins with three-dimensional (3-D) nonlinear elasticity and mathematically splits the analysis into a one-dimensional through-the-thickness analysis and a two-dimensional (2-D) plate analysis. The through-the-thickness analysis provides the 2-D constitutive law which is then given as an input to the 2-D reference surface analysis. The dimensional reduction is carried out using Variational Asymptotic Method (VAM) for moderate strains and very small thickness-to-wavelength ratio. It features the identification and utilization of additional small parameters such as ratio of thicknesses and stiffness coefficients of core and films. Closed form analytical expressions for warping functions and 2-D constitutive law of the film-fabric laminate are obtained.

Anomalous lifetime statistics of ligand-receptor binding in a tethered polymer system

In this paper, motivated by observations of non-exponential decay times in the stochastic binding and release of ligand-receptor systems, exemplified by the work of Rogers et al on optically trapped DNA-coated colloids (Rogers et al 2013 Soft Matter 9 6412), we explore the general problem of polymer-mediated surface adhesion using a simplified model of the phenomenon in which a single polymer molecule, fixed at one end, binds through a ligand at its opposite end to a flat surface a fixed distance L away and uniformly covered with receptor sites. Working within the Wilemski-Fixman approximation to diffusion-controlled reactions, we show that for a flexible Gaussian chain, the predicted distribution of times f(t) for which the ligand and receptor are bound is given, for times much shorter than the longest relaxation time of the polymer, by a power law of the form t(-1/4). We also show when the effects of chain stiffness are incorporated into this model (approximately), the structure of f(t) is altered to t(-1/2). These results broadly mirror the experimental trends in the work cited above.

Experimental Study on Dynamic Properties of High Strength Fiber Clusters

In this paper, the dynamic behaviors of several kinds of high strength fibers, including Kevlar, UHMPE, glass fibers, carbon fibers etc., are investigated experimentally, with a Split Hopkinson Tension Bar (SHTB). The effect of strain rate on the modulus, strength, failure strain and failure characteristics of fibers, under impact loading, is analyzed with the relative stress vs. strain curves. At the same time, the mechanism about the rate dependence of mechanical behaviors of various fibers is discussed based on the understanding on the microstructures and deformation models of materials. Some comments are also presented on the decentralization of experimental results, and a new method called traveling wave method is presented to increase the experimental accuracy. Research results obtained in this paper will benefit to understand the energy absorption and to build up the constitutive law of protective materials reinforced by high strength fibers.

Structural and Mechanical Properties of the Organic Matrix Layers of Nacre

The type of nanostructure referred to in biomineralization as a mineral bridge has been directly observed and measured in the organic matrix layers of nacre by transmission electron microscopy and scanning electron microscopy. Statistical analysis provides the geometric characteristics and a distribution law of the mineral bridges in the organic matrix layers. Experiments reveal that the nanostructures significantly influences the mechanical properties of the organic matrix layers. In addition, the mechanical analysis illustrates the effects of the nanostructures on the behaviors of the organic matrix layers, and the analytical results explain the corresponding experimental phenomena fairly well. The present study shows that the mineral bridges play a key role in the mechanical performances of the organic matrix layers of nacre. The results obtained provide a guide to the interfacial design of synthetic materials.

Damage evolution, localization and failure of solids subjected to impact loading

In order to reveal the underlying mesoscopic mechanism governing the experimentally observed failure in solids subjected to impact loading, this paper presents a model of statistical microdamage evolution to macroscopic failure, in particular to spallation. Based on statistical microdamage mechanics and experimental measurement of nucleation and growth of microcracks in an Al alloy subjected to plate impact loading, the evolution law of damage and the dynamical function of damage are obtained. Then, a lower bound to damage localization can be derived. It is found that the damage evolution beyond the threshold of damage localization is extremely fast. So, damage localization can serve as a precursor to failure. This is supported by experimental observations. On the other hand, the prediction of failure becomes more accurate, when the dynamic function of damage is fitted with longer experimental observations. We also looked at the failure in creep with the same idea. Still, damage localization is a nice precursor to failure in creep rupture.

A new hardening law for strain gradient plasticity

A new hardening law of the strain gradient theory is proposed in this paper, which retains the essential structure of the incremental version of conventional J(2) deformation theory and obeys thermodynamic restrictions. The key feature of the new proposal is that the term of strain gradient plasticity is represented as an internal variable to increase the tangent modulus. This feature which is in contrast to several proposed theories, allows the problem of incremental equilibrium equations to be stated without higher-order stress, higher-order strain rates or extra boundary conditions. The general idea is presented and compared with the theory given by Fleck and Hutchinson (Adv. in Appl. Mech. (1997) 295). The new hardening law is demonstrated by two experimental tests i.e. thin wire torsion and ultra-thin beam bending tests. The present theoretical results agree well with the experiment results.

Optimized Group Velocity Control Scheme and DNS of Decaying Compressible Turbulence of Relative High Turbulent Mach Number

To overcome the difficulty in the DNS of compressible turbulence at high turbulent Mach number, a new difference scheme called GVC8 is developed. We have succeeded in the direct numerical simulation of decaying compressible turbulence up to turbulent Mach number 0.95. The statistical quantities thus obtained at lower turbulent Mach number agree well with those from previous authors with the same initial conditions, but they are limited to simulate at lower turbulent Mach numbers due to the so-called start-up problem. The energy spectrum and coherent structure of compressible turbulent flow are analysed. The scaling law of compressible turbulence is studied. The computed results indicate that the extended self-similarity holds in decaying compressible turbulence despite the occurrence of shocklets, and compressibility has little effects on relative scaling exponents when turbulent Mach number is not very high.

Statistical and stochastic description of microvoid evolution observed in dynamic failure of ductile materials

A brief review is presented of statistical approaches on microdamage evolution. An experimental study of statistical microdamage evolution in two ductile materials under dynamic loading is carried out. The observation indicates that there are large differences in size and distribution of microvoids between these two materials. With this phenomenon in mind, kinetic equations governing the nucleation and growth of microvoids in nonlinear rate-dependent materials are combined with the balance law of void number to establish statistical differential equations that describe the evolution of microvoids' number density. The theoretical solution provides a reasonable explanation of the experimentally observed phenomenon. The effects of stochastic fluctuation which is influenced by the inhomogeneous microscopic structure of materials are subsequently examined (i.e. stochastic growth model). Based on the stochastic differential equation, a Fokker-Planck equation which governs the evolution of the transition probability is derived. The analytical solution for the transition probability is then obtained and the effects of stochastic fluctuation is discussed. The statistical and stochastic analyses may provide effective approaches to reveal the physics of damage evolution and dynamic failure process in ductile materials.

Energy Principle And Nonlinear Electric-Mechanical Behavior Of Ferroelectric Ceramics

Many experimental observations have shown that a single domain in a ferroelectric material switches by progressive movement of domain walls, driven by a combination of electric field and stress. The mechanism of the domain switch involves the following steps: initially, the domain has a uniform spontaneous polarization; new domains with the reverse polarization direction nucleate, mainly at the surface, and grow though the crystal thickness; the new domain expands sideways as a new domain continues to form; finally, the domain switch coalesces to complete the polarization reversal. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of the ferroelectric material and used to study the nonlinear constitutive behavior of a ferroelectric body in this paper. The principle of stationary total potential energy is put forward in which the basic unknown quantities are the displacement u(i), electric displacement D-i and volume fraction rho(I) of the domain switching for the variant I. The mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total potential energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion established by Hwang et al. [ 1]. Based on the domain switching criterion, a set of linear algebraic equations for determining the volume fraction rho(I) of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. If the volume fraction rho(I) of domain switching for each domain is prescribed, the unknown displacement and electric potential can be obtained based on the conventional finite element procedure. It is assumed that a domain switches if the reduction in potential energy exceeds a critical energy barrier. According to the experimental results, the energy barrier will strengthen when the volume fraction of the domain switching increases. The external mechanical and electric loads are increased step by step. The volume fraction rho(I) of domain switching for each element obtained from the last loading step is used as input to the constitutive equations. Then the strain and electric fields are calculated based on the conventional finite element procedure. The finite element analysis is carried out on the specimens subjected to uniaxial coupling stress and electric field. Numerical results and available experimental data are compared and discussed. The present theoretic prediction agrees reasonably with the experimental results.

Energy principle of ferroelectric ceramics and single domain mechanical model

Many physical experiments have shown that the domain switching in a ferroelectric material is a complicated evolution process of the domain wall with the variation of stress and electric field. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of ferroelectric ceramic and used to study the nonlinear constitutive behavior of ferroelectric body in this paper. The principle of stationary total energy is put forward in which the basic unknown quantities are the displacement u (i) , electric displacement D (i) and volume fraction rho (I) of the domain switching for the variant I. Mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion. On the basis of the domain switching criterion, a set of linear algebraic equations for the volume fraction rho (I) of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. Then a single domain mechanical model is proposed in this paper. The poled ferroelectric specimen is considered as a transversely isotropic single domain. By using the partial experimental results, the hardening relation between the driving force of domain switching and the volume fraction of domain switching can be calibrated. Then the electromechanical response can be calculated on the basis of the calibrated hardening relation. The results involve the electric butterfly shaped curves of axial strain versus axial electric field, the hysteresis loops of electric displacement versus electric filed and the evolution process of the domain switching in the ferroelectric specimens under uniaxial coupled stress and electric field loading. The present theoretic prediction agrees reasonably with the experimental results given by Lynch.

Statistical formulation and experimental determination of growth rate of micrometre cracks under impact loading

A new statistical formulation and a relevant experimental approach to determine the growth rate of microcracks were proposed. The method consists of experimental measurements and a statistical analysis' on the basis of the conservation law of number density of microcracks in phase space. As a practical example of the method, the growth rate of microcracks appearing in an aluminium alloy subjected to planar impact loading was determined to be ca. 10 mu m/mu s under a tensile stress of 1470 MPa and load duration between 0.26 mu s and 0.80 mu s.

Initial development of microdamage under impact loading

In this paper, the initial development of microdamage in material subjected to impulsive loading was investigated experimentally and analytically with controllable short-load duration. Based on a general solution to the statistical evolution of a one-dimensional system of ideal microcracks, a prerequisite to experimental investigation of nucleation of microcracks was derived. By counting the number of microcracks, the distribution of nucleation of microcracks was studied. The law of the nucleation rate of microcracks can be expressed as a separable function of stress and cracksize. It is roughly linear dependence on loading stress. The normalized number density of microcracks is in agreement with that of a second-phase particle.

Territorial Integrity and Self-Determination : The Approach of the International Court of Justice in the Advisory Opinion on Kosovo

[EN] On 17 February 2008 Kosovo approved its declaration of independence from Serbia. The declaration was raised as a unilateral secession, a category which to date is widely debated by the international community, but supported in that case by a respectable number of the United Nation member states. A great many legal issues have been raised by the International Court of Justice's Advisory Opinion on Kosovo. This opinion was eagerly awaited by legal scholars due to both its possible effects and the scope of its principles outside the context of decolonization in what it could constitute of new approach to the international scenario for the twenty-first century. The ICJ stated that the declaration of independence was in accordance with international law if it was not prohibited. The answer turned on whether or not international law prohibited the declaration of independence, without ever examining whether an entity seeking secession is entitled with a positive right to secede and if so, under which circumstances. The basic issue can be summarised as whether or not we are facing a new course in the interpretation of certain classical categories of international law: the principle of territorial integrity, statehood, sovereignty, recognition, the right to external self-determination, etc. In this study we shall analyse some of the aspects arising from the Advisory Opinion of the International Court of Justice on the Accordance with international law of the unilateral declaration of independence in respect of Kosovo focusing on the territorial issue. Firstly we shall analyse the scope of the principle of territorial integrity of States and how it operates ; secondly, we shall focus on the scope of that principle in relation to the interior of the State, and ask ourselves how international law operates in relation to declarations of independence. Lastly, we shall deal with the principle of respect for territorial integrity in the specific case of Serbia with respect to Kosovo, and then end with a series of general conclusions. This study aims, definitely, to contribute to the theoretical debate on the challenges to the traditional certainties of international law in this area.

Fishery resources of the United States of America

The term “fishery resources” is used in this book with a broad application. It includes the populations of the fishes and other organisms useful to men, the environment that makes life possible for them, the industry that exploits and utilizes them, and our knowledge about them by which we can conserve their productivity. This book aims to survey the present status of all these aspects of those fishery resources that are used or are available for use by United States anglers and commercial fishermen. It is planned primarily for the Congress, at its request, with the idea of giving to busy people, in condensed fashion, a perspective on its subject. (pdf contains 142 pages)

Friction properties of bio-mimetic nano-fibrillar arrays

Nano-fibrillar arrays are fabricated using polystyrene materials. The average diameter of each fiber is about 300 nm. Experiments show that such a fibrillar surface possesses a relatively hydrophobic feature with a water contact angle of 142 degrees. Nanoscale friction properties are mainly focused on. It is found that the friction force of polystyrene nano-fibrillar surfaces is obviously enhanced in contrast to polystyrene smooth surfaces. The apparent coefficient of friction increases with the applied load, but is independent of the scanning speed. An interesting observation is that the friction force increases almost linearly with the real contact area, which abides by the fundamental Bowden-Tabor law of nano-scale friction.