A UNIFIED ENERGY APPROACH TO A CLASS OF MICROMECHANICS MODELS FOR COMPOSITE MATERIALS

Several micromechanics models for the determination of composite moduli are investigated in this paper,including the dilute solution,self-consistent method,generalized self-consistent method,and Mori-Tanaka's method.These mi- cromechanical models have been developed by following quite different approaches and physical interpretations.It is shown that all the micromechanics models share a common ground,the generalized Budiansky's energy-equivalence framework.The dif- ference among the various models is shown to be the way in which the average strain of the inclusion phase is evaluated.As a bonus of this theoretical development,the asymmetry suffered in Mori-Tanaka's method can be circumvented and the applica- bility of the generalized self-consistent method can be extended to materials contain- ing microcracks,multiphase inclusions,non-spherical inclusions,or non-cylindrical inclusions.The relevance to the differential method,double-inclusion model,and Hashin-Shtrikman bounds is also discussed.The application of these micromechanics models to particulate-reinforced composites and microcracked solids is reviewed and some new results are presented.

岩石变形破坏局部化的白光数字散斑相关方法研究(英文)

介绍了白光数字散斑法的基本原理 ,并采用白光数字散斑相关方法研究了煤岩的变形局部化 ,通过实验测定了煤岩变形局部化的开始时刻、演化过程 ,首次获得了局部化带的宽度 ,为研究岩石非均匀变形的演化过程。

Novel implementation of homogenization method to predict effective properties of periodic materials

Representative volume element （RVE） method and asymptotic homogenization （AH） method are two widely used methods in predicting effective properties of pe- riodic materials. This paper develops a novel implementa- tion of the AH method, which has rigorous mathematical foundation of the AH method, and also simplicity as the RVE method. This implementation can be easily realized using commercial software as a black box, and can use all kinds of elements available in commercial software to model unit cells with rather complicated microstructures, so the model may remain a fairly small scale. Several examples were car- fled out to demonstrate the simplicity and effectiveness of the new implementation.

THE ANALYTICAL APPROACH FOR LARGE SCALE NON-CLASSICALLY DAMPED DYNAMIC SYSTEM

This paper gives a dynamic decoupling approach for the analysis of large scale non-classically damped system, in which the complex variable computations were completely avoided not only in solving for the eigenvalue problem but also in the calculation of the dynamic response. The analytical approaches for undamped gyroscopic system, non-classically damped system, including the damped gyroscopic system were unified. Very interesting and useful theoretical results, practical algorithms were obtained which are applicable to both non-defective and defective systems.

STUDY OF THERMAL DEFORMATION OF MICROELECTRONICS PACKAGING PRODUCT BY INTERFEROMETRIC TECHNIQUE

In this paper, the out-of-plane deformation of silicon surface of Direct Chip Attachment (DCA) assembly, under thermal loading, was measured in real-time by Twyman/Green interferometry. The contour maps of the out-of-plane displacement fields of silicon surface under thermal loading and cycling of various temperature were obtained, Experimental results show that the relation between the out-of-plane displacement and temperature is nonlinear and varies with temperature cycling, due to nonlinear mechanical behavior of the materials used in electronic packaging. A comparison of the aut-of-plane displacement Gelds of silicon surface measured by T/G interferometry in real-time and replicating technique of high temperature specimen grating of moire interferometry was made.

A NEW METHOD FOR THE UNCERTAIN RESPONSE ANALYSIS OF STRUCTURES WITH UNCERTAIN PARAMETERS

A computing method for estimating the upper and lower bounds of the response of structures with uncertainties is presented. The uncertain parameters are described by the convex model. A numerical example of the frame structure is given to illustrate the effectiveness of this method.

DAMPING COMPUTATION OF LIQUID SLOSHING IN CONTAINERS ABOARD SPACECRAFT

Under the non-rotating assumption, a method for the calculation of damping of fuel sloshing with small amplitude in containers aboard spacecraft is proposed in the present paper. And we have presented an eigen-value equation for sloshing damping and frequency computation. This equation may be solved by Ritz or Galerkin methods for a container of simple geometry or by finite element method for a container of arbitrary geometric shape even with rigid baffles. The simulated results show that the equivalent damping coefficients is directly proportional to fuel's viscosity, whereas it almost exhibits no influence on sloshing frequencies. The drawback of the proposed method lies in expensive computation cost. Thus far, it hasn't yet be applied to a container with elastic baffles.

Semi-analytical method for calculating aeroelastic effect of profiled rod flying at high velocity

The key technique of a kinetic energy rod(KER) warhead is to control the flight attitude of rods. The rods are usually designed to different shapes. A new conceptual KER named profiled rod which has large L/D ratio is described in this paper. The elastic dynamic equations of this profiled rod flying at high velocity after detonation are set up on the basis of Euler-Bernoulli beam, and the aeroelastic deformation of profiled rod is calculated by semi-analytical method for calculating the vibration characteristics of variable cross-section beam. In addition, the aeroelastic deformation of the undeformed profiled rod and the aeroelastic deformation of deformed profiled rod which is caused by the detonation of explosive are simulated by computational fluid dynamic and finite element method(CFD/FEM), respectively. A satisfactory agreement of these two methods is obtained by the comparison of two methods. The results show that the semi-analytical method for calculating the vibration characteristics of variable cross-section beam is applied to analyze the aeroelastic deformation of profiled rod flying at high velocity.

LARGE RANGE ANALYSIS FOR NONLINEAR DYNAMIC SYSTEMS——ELEMENT MAPPING METHOD

This paper presents a new method for global analysis of nonlinear system. By means of transforming the nonlinear dynamic problems into point mapping forms which are single-valued and continuous, the state space can be regularly divided into a certain number of finitely small triangle elements on which the non-linear mapping can be approximately substituted by the linear mapping given by definition. Hence, the large range distributed problem of the mapping fixed points will be simplified as a process for solving a set of linear equations. Still further, the exact position of the fixed points can be found by the iterative technique. It is convenient to judge the stability of fixed points and the shrinkage zone in the state space by using the deformation matrix of linear mapping. In this paper, the attractive kernel for the stationary fixed point is defined, which makes great advantage for describing the attractive domains of the fixed points. The new method is more convenient and effective than the cell mapping method. And an example for two-dimensional mapping is given.

NONLINEAR DYNAMIC RESPONSE AND DYNAMIC BUCKLING OF SHALLOW SPHERICAL SHELLS WITH CIRCULAR HOLE

In this paper, the nonlinear equations of motion for shallow spherical shells with axisymmetric deformation including transverse shear are derived. The nonlinear static and dynamic response and dynamic buckling of shallow spherical shells with circular hole on elastically restrained edge are investigated. By using the orthogonal point collocation method for space and Newmarh-β scheme for time, the displacement functions are separated and the nonlinear differential equations are replaced by linear algebraic equations to seek solutions. The numerical results are presented for different cases and compared with available data.

STUDY OF CONSTITUTIVE RELATIONS FOR PSEUDO-ELASTICITY AND SHAPE MEMORY BEHAVIOR

Constitutive relations are given for the description of the deformation behavior of shape memory materials. The deformation is the superposition of the elastic, the thermal and the phase transformation deformation caused by the transformation from one to the other among the high temperature phase, the low temperature phase and the stress induced phase. The phase transformation is controlled by the driving force, i.e., the Gibbs energy difference between the phases.

THE NONLINEAR INTERACTION OF VORTEX RINGS WITH A FREE SURFACE

Nonlinear interactions of vortex rings with a free surface are considered in an incompressible, ideal fluid using the vortex contour dynamics technique and the boundary integral equation method. The flow is axisymmetric and the vorticity is linearly distributed in the vortex. Effects of the gravity and the surface tension as well as the initial geometric parameter of the vortex on the interaction process are investigated in considerable detail. The interaction process may be divided into three major stages: the vortex free-traveling stage, the collision stage, and the vortex stretching and rebounding stage. Time evolutions of both the vortex and free surface under various conditions are provided and analyzed. Two kinds of waves exist on the free surface during interaction. In a special case where the gravity and surface tension are very weak or the vortex is very strong, an electric-bulb-like 'cavity' is formed an the free surface and the vortex is trapped in the 'cavity' for quite a. long time, resulting in a large amount, of fluid above the mean fluid surface.

A NEW APPROXIMATE SOLUTION TO THE MULTIPLE SCATTERING THEORY FOR THE ELASTIC PROPERTIES OF HETEROGENEOUS MATERIALS

The multiple scattering theory has been a powerful tool in determining the effective properties of heterogeneous materials. In this paper , a simple relationship between the scattering theory and the micromechanics theory based on the Eshelby principle has been suggested. According to the relationship, a new and simple approximate solution to the exact multiple scattering theory has been given in terms of Eshelby' s S-tensor. The solution easily shows those known results for isotropic composites with spherical inclusions and for tracnsversely isotropic composites, and first gives non-setf-consistent (average t-matrix) and symmetric self-consistent (effective medium or coherent potential) approximate results for isotropic composites with spheroidal inclusions.

Correlation of the positive stress ratio effects on fatigue crack propagation rate of aluminium alloys based on a new parameter da/dS

In-situ SEM (Scanning Electron Microscope) observation of fatigue crack propagation in aluminium alloys reveals that crack growth occurs in a continuous way over the time period during the load cycle. Based on this observation, a new parameter da/dS is introduced to describe the fatigue crack propagation rate, which defines the fatigue crack propagation rate with the change of the applied stress at any moment of a stress cycle. The relationship is given between this new parameter and the conventional used parameter da/dN which describes the fatigue crack propagation rate per stress cycle. Using this new parameter, an analysis has been performed and a model has been set up to consider the effect of the applied stress ratio on the fatigue crack propagation rate. The obtained results have been used to correlate the published test data and a good correlation has been achieved. This method is very easy to use and no fatigue crack closure measurement is needed, therefore this model is significant in engineering application.

BIFURCATION CURVES OF THE HÉNON MAP DETERMINED BY A MULTIPLE-SHOOTING TECHNIQUE

A multiple shooting method combined with a Newton iteration for determining bifurcation curves of two-dimensional maps is presented.This method is so effective that the high period bifurcation curves which could not be estimated with any other methods can be determined.Some P8 bifurcation curves of the Henon map are calculated as an example.

A SURVEY OF WORKS ON THE THEORY OF TOROIDAL SHELLS AND CURVED TUBES

This paper gives a survey of works on the theory of toroidal shells which were done by our two universities in recent years.

ON THE PROPERTIES OF ELASTIC-VISCOUS FLUID FLOW PAST AN OBSTACLE

Fundamental equations for the analysis of plane flow of elastic-viscous fluid are established. On such a basis, a perturbed-weighted residual finite element model for small Deborah number situations is formulated. The model is further incorporated for investigations on the behavioral characteristics of the elastic-viscous fluid flow when passing an obstacle, which include the mechanisms of the retardation of separation point, and the reduction of drag forces and so forth. The numerical investigations demonstrate the favorable advantages of the present model in its remarkable simplicity and reasonable accuracy attained in plane flow analysis.

A FINITE DIFFERENCE METHOD AT ARBITRARY MESHES FOR THE BENDING OF PLATES WITH VARIABLE THICKNESS

A finite difference method at arbitrary meshes for the bending of plates with variable thickness is presented in this paper. The method is completely general with respect to various boundary conditions, load cases and shapes of plates. This difference scheme is simple and the numerical results agree well with those obtained by other methods.

RECENT PROGRESS IN NONLINEAR EDDY-VISCOSITY TURBULENCE MODELING

This article presents recent progresses in turbulence modeling in the Unit for Turbulence Simulation in the Department of Engineering Mechanics at Tsinghua University. The main contents include: compact Non-Linear Eddy-Viscosity Model (NLEVM) based on the second-moment closure, near-wall low-Re non-linear eddy-viscosity model and curvature sensitive turbulence model.The models have been validated in a wide range of complex flow test cases and the calculated results show that the present models exhibited overall good performance.