Analysis of elastoplastic deformation in metal-matrix composites with particulate reinforcements

In this paper, elastoplastic stress-strain behavior during tensile deformation of an aluminum alloy matrix composite containing alumina circular and non-circular particles is analyzed. In terms of cell models in conjunction with continuum plasticity theory, various periodic arrays of particles are assumed in a three-dimensional finite element simulation. The geometrical effects of particle volume fraction, shape, aspect ratio, array and distribution, as well as non-circular particle orientation on the overall elastoplastic stress-strain behavior are examined in view to design optimum microstructures of the composites. The project supported by the National Natural Science Foundation of China and the State Education Commission of China     

A FINITE ELEMENT—MATHEMATICAL PROGRAMMING METHOD FOR ELASTOPLASTIC PROBLEMS BASED ON THE PRINCIPLE OF VIRTUAL WORK

By expanding the yielding function according to Taylor series and neglecting the high order terms, the elastoplastic constitutive equation is written in a linear complementary form. Based on this linear complementary form and the principle of virtual work, a finite element-complementary method is derived for elastoplastic problem. This method is available for materials which satisfy either associated or nonassociated flow rule. In addition, the existence and uniqueness of solution for the method are also discussed and some useful conclusions are given. The project is supported by the National Natural Science Foundation of China     

Elastoplastic model describing cyclic creeping behaviour of soft clays

The elastoplastic model in the deviatoric stress space is constructed to describe the cyclic undrained creeping behaviour of soft clays under cyclic stress by using Mises yield criterion and the concept of a field of hardening moduli. Furthermore, the effect of model parameters on the deformation is studied, and a method is given to determine quantitatively model parameters from results of cyclic triaxial tests of the saturated soft clay. The project supported by National Natural Science Foundation of China and Tianjin Twenty-one Century Youth Science Foundation     

Boundary element analysis for elastic and elastoplastic problems of 2D orthotropic media with stress concentration

Both the orthotropy and the stress concentration are common issues in modern structural engineering. This paper introduces the boundary element method (BEM) into the elastic and elastoplastic analyses for 2D orthotropic media with stress concentration. The discretized boundary element formulations are established, and the stress formulae as well as the fundamental solutions are derived in matrix notations. The numerical procedures are proposed to analyze both elastic and elastoplastic problems of 2D orthotropic media with stress concentration. To obtain more precise stress values with fewer elements, the quadratic isoparametric element formulation is adopted in the boundary discretization and numerical procedures. Numerical examples show that there are significant stress concentrations and different elastoplastic behaviors in some orthotropic media, and some of the computational results are compared with other solutions. Good agreements are also observed, which demonstrates the efficiency and reliability of the present BEM in the stress concentration analysis for orthotropic media. The project supported by the Basic Research Foundation of Tsinghua University, the National Foundation for Excellent Doctoral Thesis (200025) and the National Natural Science Foundation of China (19902007). The English text was polished by Keren Wang.     

Analysis of interlaminar stress and nonlinear dynamic response for composite laminated plates with interfacial damage

By considering the effect of interfacial damage and using the variation principle, three-dimensional nonlinear dynamic governing equations of the laminated plates with interfacial damage are derived based on the general sixdegrees-of-freedom plate theory towards the accurate stress analysis. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are obtained by using the finite difference method, and the results are validated by comparison with the solution of nonlinear finite element method. In numerical calculations, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed.     

The crack tip zone shielding effect for ductile particle reinforced brittle materials

The crack tip zone shielding effect for the ductile particle reinforced brittle materials is analyzed by using a micromechanics constitutive theory. The theory is developed here to determine the elastoplastic constitutive behavior of the composite. The elastoplastic particles, with isotropic or kinematical hardening, are uniformly dispersed in the brittle elastic matrix. The method proposed is based on the Mori-Tanaka's concept of average stress in the composite. The macroscopic yielding condition and the incremental stress strain relation of the composite during plastic deformation are explicity given in terms of the macroscopioc applied stress and the microstructural parameters of the composite such as the volume fraction and yield stress of ductile particles, elastic constants of the two phases, etc. Finally, the contribution of the plastic deformation in the particles near a crack tip to the toughening of the composite is evaluated. The project supported by National Natural Science Foundation of China     

A class of singularly perturbed reaction diffusion systems

A class of singularly perturbed reaction diffusion systems are considered. Under suitable conditions, using the comparison theorem the asymptotic behavior of solution for the initial boundary value problems is studied. Project supported by the National Natural Science Foundation of China     

On the initial value problems of first order impulsive differential systems

The purpose of this paper is to study the existence and iterative approximation of minimax quasi-solutions for a class of initial value problems of first order impulsive differential systems by using monotone iterative methods. Project supported by the National Natural Science Foundation of China     

Coupling effects of void size and void shape on the growth of prolate ellipsoidal microvoid

The combined effects of void size and void shape on the void growth are studied by using the classical spectrum method. An infinite solid containing an isolated prolate spheroidal void is considered to depict the void shape effect and the Fleck-Hutchinson phenomenological strain gradient plasticity theory is employed to capture the size effects. It is found that the combined effects of void size and void shape are mainly controlled by the remote stress triaxiality. Based on this, a new size-dependent void growth model similar to the Rice-Tracey model is proposed and an important conclusion about the size-dependent void growth is drawn: the growth rate of the void with radius smaller than a critical radius r_c may be ignored. It is interesting that r_c is a material constant independent of the initial void shape and the remote stress triaxiality.The project supported by the National Natural Science Foundation of China (A10102006) and the New Century Excellent Talents in Universities of China. The English text was polished by Keren Wang.     

ON THE WELL POSEDNESS OF INITIAL VALUE PROBLEM FOR EULER EQUATIONS OF INCOMPRESSIBLE INVISCID FLUID(Ⅱ)

The solvability of the Euler equations about incompressible inviscid fluid based on the stratification theory is discussed. And the conditions for the existence of formal solutions and the methods are presented for calculating all kinds of ill-posed initial value problems. Two examples are given as the evidences that the initial problems at the hyper surface does not exist any unique solution. Foundation item: the National Natural Science Foundation of China (19971054) Biography: Shen Zhen (1977−)     

A note for analysis of thermo-mechanical contact problems

A discussion about the bifurcation and non-uniqueness of solutions in the analysis of thermo-mechanical contact problems with initial gap is given. Without loss of generality, a mechanical contact problem coupled with steady heat transfer is studied and an example of non-uniqueness of solutions caused by the thermo-mechanical mechanism is presented. The important work is that the non-uniqueness of solutions, which is different from that found in the analysis of the traditional frictional contact problems, is studied in detail. The possible oscillation and non-convergence problems in the iteraction process of the numerical computation are discussed, and an enhanced algorithm is put forward to overcome the difficulties. Project sypported by the National Natural Science Foundation of China (Nos. 50178016, 10225212 and 19872016), the National Key Basic Research Special Foundation (No. G1999032805) and the Foundation for University Key Teacher by the Ministry of Education.     

On the formal solution of initial value problem of Navier-Stokes equation

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P-version hybrid analytical finite element method for plate bending problems

Two sets of trial functions with different variables are constructed for the admissible space of the finite element analysis. The trial functions satisfy the equilibrium differential equation inside elements, while the deflections and rotations on the edges of the elements are approximated by the Peano hierarchical interpolation functions. Then, a generalized variational principle is applied to set up the p-version hybrid analytical finite element method for plate bending problems. The accuracy of finite element computation can be improved by increasing the order of the interpolation polynomials with fixed mesh. In the finite element formulation, to obtain the stiffness matrices and the load vectors, it is only necessary to perform quadrature over the edges of the elements. These matrices and vectors possess an embedding structure. The conformability between the elements can be controlled automatically.This work is supported by the Natural Science Foundation of China and the Aeronautical Science Foundation of China.     

The growth of the void in a hyperelastic rectangular plate under a uniaxial extension

In the present paper, the finite deformation and stress analysis for a hyperelastic rectangular plate with a center void under a uniaxial extension is studied. In order to consider the effect of the existence of the void on the deformation and stress of the plate, the problem is reduced to the deformation and stress analysis for a hyperelastic annular plate and its approximate solution is obtained from the minimum potential energy principle. The growth of the cavitation is also numerically computed and analysed.Project supported by the National Natural Science Foundation of China     

A STUDY OF THE INFLUENCE OF INTERFACIAL DAMAGE ON STRESS CONCENTRATIONS IN INTRAPLY HYBRID COMPOSITES

In the axial tensile failure process of intraply hybrid composites, the breakage of some fibers may lead to interfacial damage, thus directly influencing the local stress concentrations near the sites of breakage. A modified shear-lag model, in which the interfacial damage is considered, is proposed. Based on the model, the influence of interfacial shear strength on the stress concentrations and the lengths of interfacial damage zone is first studied. The present results also provide an important theoretical basis for investigating the failure mechanism and hybrid effects for such kind of composites. Project supported by the National Natural Science Foundation of China (No. 199902004) and Guangdong Provincial Natural Science Foundation (No. 000391).     

Application of finite difference method adopted in fluid mechanics to sound propagation in ducts

Researches on sound propagation problems in ducts done by the author and other investigators in recent years are briefly discussed in this paper. The finite difference method used in fluid mechanics is used for solving these problems thus presenting an aspect of the development of research work in this field at home and abroad.The project supported by National Natural Science Foundation of China.     

Some applications of boundary element methods, boundary element-finite element coupling techniques in elasto-plastic stress analysis

In this paper some research works of author's group on boundary element method for linear elastic and elasto-plastic problems are briefly summarized. The BE subrogions method and BE-FE coupling techniques are introduced, and some idea of the error estimation of BE solutions is presented.This work is supported by the National Natural Science Foundation of China.     

The instability of the diffusion-controlled grain-boundary void in stressed solid

As atoms migrate along a void surface and grain-boundary, driven by various thermodynamic forces, the grain-boundary void changes its shape and volume. When the void changes its configuration, the free energy of the system also changes. In this article, the free energy is calculated for an evolving grain-boundary void filled with gas in a stressed solid. Then the instability conditions and the equilibrium shape of the void are determined as a function of the grain-boundary and surface energies, the void volume, the externally applied stresses, as well as the internal pressure built up by the gas filled in the void. The project supported by the National Natural Foundation of China (10272075 and 19972053)     

An improved formulation for domain stress evaluation by boundary element method in elastoplastic problems

An integral expression for domain stresses in the elastoplastic boundary element method is presented. Thus it is not necessary to evaluate the Cauchy. principal value in domain integral. This method shows some improvement in the accuracy and efficiency for the numerical process. A numerical result of axisymmetric elastoplastic problem has been worked out and a comparison with analytical result is given.This work had been supported by National Science Foundation of China.     

The effect of straining mode on void growth

Large strain finite element method is employed to investigate the effect of straining mode on void growth. Axisymmetric cell model embedded with spherical void is controlled by constant triaxiality loading, while plane-stress model containing a circular void is loaded by constant ratio of straining. Elastic-plastic material is used for the matrix in both cases. It is concluded that, besides the known effect of triaxiality, the straining mode which intensifies the plastic concentration around the void is also a void growth stimulator. Experimental results are cited to justify the computation results. This paper is jointly supported by the National Natural Science Foundation of China (19872064), the Chinese Academy of Sciences (KJ951-1-201) and the Laboratory for Nonlinear mechanics of Continuous Media of the Institute of Mechanics