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.

Hill Instability Analysis Of Tlp Tether Subjected To Combined Platform Surge And Heave Motions

This paper presents the Hill instability analysis of Tension Leg Platform (TLP) tether it, deep sea. The 2-D nonlinear beam model which is Undergoing Coupled axial and transverse vibrations, is applied. The governing equations are reduced to nonlinear Hill equation by use of the Galerkin's method and the modes superposition principle. The Hill instability charted Lip to large parameters is obtained. An important parameter M is defined and can he expressed as the functions of tether length, the platform surge and heave motion amplitudes. Some example studies are performed for various environmental conditions. The results demonstrate that the nonlinear coupling between the axial and transverse vibrations has a significant effect on the response of structure.. It needs to be considered for the accurate dynamic analysis of long TLP tether subjected to the combined platform surge and heave motions.

Influence Of Rayleigh Effect Combined With Marangoni Effect On The Onset Of Convection In A Liquid Layer Overlying A Porous Layer

The coupling mechanism of Rayleigh effect and Marangoni effect in a liquid-porous system is investigated using a linear stability analysis. The eigenvalue problem is solved by means of a Chebyshev tau method. Results indicate that there are three coupling modes between the Rayleigh effect and the Marangoni effect for different depth ratios. (C) 2008 Elsevier Ltd. All rights reserved.

First-passage time of Duffing oscillator under combined harmonic and white-noise excitations

The first-passage time of Duffing oscillator under combined harmonic and white-noise excitations is studied. The equation of motion of the system is first reduced to a set of averaged Ito stochastic differential equations by using the stochastic averaging method. Then, a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. Finally, the conditional reliability function, and the conditional probability density and moments of first-passage time are obtained by solving the backward Kolmogorov equation and generalized Pontryagin equations with suitable initial and boundary conditions. Numerical results for two resonant cases with several sets of parameter values are obtained and the analytical results are verified by using those from digital simulation.

Adsorption of human serum albumin onto gold: a combined electrochemical and ellipsometric study

Human serum albumin adsorption onto gold surfaces was investigated by electrochemical and ellipsometric methods. Albumin adsorption onto gold was confirmed by the change of the open circuit potential of gold and by the ellipsometric parameter variation during albumin immobilization. In both experiments the parameters reached stable values within 10-15 min. The albumin adsorption layer thickness measured with the ellipsometer was about 1.5 nm. The adsorption of albumin Under applied potential was also investigated and it was found that both positive and negative applied potential promote albumin adsorption. Changes in the optical parameters of bare gold and albumin adsorbed onto gold surface under applied potential were investigated with in Situ ellipsometry. The similarity and reversibility of the optical changes showed that adsorbed albumin was stable on the gold surface Under the applied potential range (-200-600 mV). The cyclic voltammograms of K3Fe(CN)(6) on the modified gold surface showed that albumin Could partly block the oxidation and reduction reaction. (C) 2004 Elsevier Inc. All rights reserved.

Optimal bounded control of first-passage failure of strongly non-linear oscillators under combined harmonic and white-noise excitations

A procedure for designing the optimal bounded control of strongly non-linear oscillators under combined harmonic and white-noise excitations for minimizing their first-passage failure is proposed. First, a stochastic averaging method for strongly non-linear oscillators under combined harmonic and white-noise excitations using generalized harmonic functions is introduced. Then, the dynamical programming equations and their boundary and final time conditions for the control problems of maximizing reliability and of maximizing mean first-passage time are formulated from the averaged Ito equations by using the dynamical programming principle. The optimal control law is derived from the dynamical programming equations and control constraint. Finally, the conditional reliability function, the conditional probability density and mean of the first-passage time of the optimally controlled system are obtained from solving the backward Kolmogorov equation and Pontryagin equation. An example is given to illustrate the proposed procedure and the results obtained are verified by using those from digital simulation. (C) 2003 Elsevier Ltd. All rights reserved.

Centrifugal experimental study of suction bucket foundations under dynamic loading

Centrifugal experiments were carried out to investigate the responses of suction bucket foundations under horizontal and vertical dynamic loading. It is shown that when the loading amplitude is over a critical value, the sand at the upper part around the bucket is softened or even liquefied. The excess pore pressure decreases from the upper part to the lower part of the sand layer in the vertical direction and decreases radially from the bucket's side wall in the horizontal direction. Large settlements of the bucket and the sand layer around the bucket are induced by dynamic loading. The dynamic responses of the bucket with smaller height (the same diameter) are heavier.

A constitutive model for cavitation and cavity growth in rubber-like materials under arbitrary tri-axial loading

In this paper, we attempted to construct a constitutive model to deal with the phenomenon of cavitation and cavity growth in a rubber-like material subjected to an arbitrary tri-axial loading. To this end, we considered a spherical elementary representative volume in a general Rivlin's incompressible material containing a central spherical cavity. The kinematics proposed by [Hou, H.S., Abeyaratne, R., 1992. Cavitation in elastic and elastic-plastic solids. J. Mech. Phys. Solids 40, 571-722] was adopted in order to construct an approximate but optimal field. In order to establish a suitable constitutive law for this class of materials, we utilized the homogenisation technique that permits us to calculate the average strain energy density of the volume. The cavity growth was considered through a physically realistic failure criterion. Combination of the constitutive law and the failure criterion enables us to describe correctly the global behaviour and the damage evolution of the material under tri-axial loading. It was shown that the present models can efficiently reproduce different stress states, varying from uniaxial to tri-axial tensions, observed in experimentations. Comparison between predicted results and experimental data proves that the proposed model is accurate and physically reasonable. Another advantage is that the proposed model does not need special identification work, the initial Rivlin's law for the corresponding incompressible material is sufficient to form the new law for the compressible material resulted from cavitation procedure. (C) 2007 Elsevier Ltd. All rights reserved.

Snap-through and pull-in instabilities of an arch-shaped beam under an electrostatic loading

The snap-through and pull-in instabilities of the micromachined arch-shaped beams under an electrostatic loading are studied both theoretically and experimentally. The pull-in instability that results in a system collision with an electrode substrate may lead to a system failure and, thus, limits the system maximum displacement. The beam/plate structure with a flat initial configuration under an electrostatic loading can only experience the pull-in instability. With the different arch configurations, the structure may experience either only the pull-in instability or the snap-through and pull-in instabilities together. As shown in our computation and experiment, those arch-shaped beams with the snap-through instability have the larger maximum displacement compared with the arch-shaped beams with only the pull-in stability and those with the flat initial configuration. The snap-through occurs by exerting a fixed load, and the structure experiences a discontinuous displacement jump without consuming power. Furthermore, after the snap-through jump, the structures are demonstrated to have the capacity to withstand further electrostatic loading without pull-in. Those properties of consuming no power and increasing the structure deflection range without pull-in is very useful in microelectromechanical systems design, which can offer better sensitivity and tuning range.