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2004 Vol. 34, No. 4

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HETEROGENEOUS MATERIALS MECHANICS: CONCEPTS AND RESEARCH DIRECTIONS
2004, 34(4): . doi: 10.6052/1000-0992-2004-4-J2004-135
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Eight research topicsof the cutting-edge, which include multiscale modeling schemes, novelcomputational schemes, nanomechanics, stochastic mechanics of microstructures,nonlocal theories and implementation, materials design, cellularmaterials, in-situconstituent material property/behavior estimation are discussed in this paper. Thisintroduction based on the presentations and penal discussions at theICHMM is tointroduce the new concepts and research directions developed at theICHMM, which isto bring forth the science in interdisciplinary fields of materials science and solidmechanics in an integrated fashion and to emphasize a more in-depth understandingof the fundamentals of the broad theme of heterogeneous materials mechanics.
Contents of Advances in Mechanics,Vol.34,2004
2004, 34(4): . doi: 10.6052/1000-0992-2004-4-J2004-169
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Subject Index to Advances in Mechanics,Vol.34,2004
2004, 34(4): . doi: 10.6052/1000-0992-2004-4-J2004-170
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Devoting his whole life to science, having his students all over the world---to celebrate the 80th anniversary of T Y Wu's birthday
2004, 34(4): 433-436. doi: 10.6052/1000-0992-2004-4-J2004-161
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2004, 34(4): 436-436. doi: 10.6052/1000-0992-2004-4-J2004-176
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ADVANCES IN NATURAL ELEMENT METHOD
2004, 34(4): 437-445. doi: 10.6052/1000-0992-2004-4-J2003-086
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The natural element method (NEM) is a new numerical computational method based on Voronoi diagramand Delaunay triangulation. It is a Galerkin-based meshless method that is builtupon the notion of the natural neighbor interpolation. The naturalelement method has advantages of both finiteelement method and meshless method, and does not have theirdisadvantages. As its shape functionssatisfy interpolating properties, the natural element method is similarto the finite element method and canexactly interpolate piece-wise linear boundary conditions. Themeshless methods, based on moving least square approximation as trialand test functions, can always exactly reproduce essential boundaryconditions. As a meshless method, the natural element method caneasily treat some problems, such as moving boundary and large deformation problems, which finiteelement method is difficult to treat. The essential difference of the natural element method and othernumerical methods is their trial and test functions. Using the natural neighbor interpolation in a Galerkinprocedure, we obtain the natural element Galerkin method based on Voronoi Structure. There are twonatural neighbor interpolants: natural neighbor-based Sibson interpolation and Laplace interpolation(non-Sibsonian interpolation). Laplace interpolation is easier than Sibson interpolation in computation.In its numerical implementation, the natural element method based on Laplace interpolation as trial and testfunctions is easier than that based on Sibson interpolation.In this paper, the basic ideas of natural neighbor-based interpolationand the natural element methodbased on Voronoi structure are presented. The recent advances in the natural neighborinterpolation and the natural element method are reviewed. Someproblems that have to be solved for NEM in the futureare discussed.
NUMERICAL MANIFOLD METHOD AND ITS APPLICATIONS IN ROCK MECHANICS
2004, 34(4): 446-454. doi: 10.6052/1000-0992-2004-4-J2003-030
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The Numerical Manifold Method (NMM) is one of important numerical methods tomodel rock mechanics problems at present. The NMM comes from the discontinuousdeformation analysis, and is mainly used to combine continuous and discontinuous mechanicsinto a system. Two meshes are employed in the method: the mathematical meshenables the nodes to build a finite cover system of the solution domain and theweighted functions, while the physical mesh provides the sub-domains of integration.The mathematical mesh is used to form mathematical covers. The physical covers aredefined by the intersection of the mathematical covers and the physical mesh. And anelement in the manifold method is defined by the intersection of physical covers. Theadvantages of the NMM are that the mathematical mesh and the physical mesh aregenerally independent, and that the manifold element is different from the finite element,and the mathematical mesh can be easily re-meshed to obtain a better accuracy ofthe solution. The NMM can simulate the open and close process of crack in thefractured rockmass due to the fact that the kinematics theory of theblock system is considered in it. Therefore themethod has been widely used in rock mechanics, and has been studied by manyscholars in recent years. In the paper, the advances of the numerical methods of thefractured rockmass from continuous to discontinuous domains are discussed. Thecomponents of the numerical manifold method and its applications in rock mechanicsand the advances in corresponding fields are discussed in detail. Finally, someproblems, such as the NMM for three-dimension problems, physical nonlinearproblems, crack propagation, related coupled methods etc., are discussed.
THE STATE-OF-THE-ART OF INCOMPATIBLE MODE OF NON-LINEAR FEM AND THE ISSUES
2004, 34(4): 455-462. doi: 10.6052/1000-0992-2004-4-J2003-080
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It is difficult and has been research focusto improve the accuracy and performance of the low order elements widely usedin non-linear FEM analysis using incompatible mode. In this paper, the basic principles of EAS(The Enhanced Assumed Strain) method are systematically summarized, and the conditions toguarantee calculation convergence, the solution stability and the construction methods of theenhanced assumed strain interpolating function are elaborated in detail. The research methods andachievements about the incompatible mode geometrically non-linear FEM inChina are reviewed, which include: 1) a convergence criteria of incompatible mode geometrically non-linear FEMwas proposed based on Hellinger-Reissner generalized variationalprinciple, and the simplified modelof incompatible geometrically non-linear FEM was constructed by using some simplifiedmethods; 2) a class of non-linear generalized variational principles wasproposed, in which thecompatible conditions between elements are relaxed. The incompatible models can be constructedby selecting incompatible functions without satisfying compatible conditions prior and theconvergence can be guaranteed. The C1 or C0 geometrically non-linear generalized hybrid elements,C1 or C0 refined hybrid elements and directly refined stiffness methodscan be constructed by applying thenon-linear generalized variational principles. The problems with respectto the application of EAS methodin the non-linear FEM analysis are pointed out, that is, the restriction of constitutive lawsand the solving methods. Furthermore, the application prospect of the incompatible modenon-linear FEM is discussed.
2004, 34(4): 463-476. doi: 10.6052/1000-0992-2004-4-J2003-111
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PROGRESS OF GEOMETRIC DYNAMICS OF NON-HOLONOMIC CONSTRAINED MECHANICAL SYSTEMS: LAGRANGE THEORY AND OTHERS
2004, 34(4): 477-492. doi: 10.6052/1000-0992-2004-4-J2003-031
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In recent ten years,nonholonomic mechanics develops mainly in two associated directions. One isnonholonomic motion planning, the other is geometric dynamics ofnonholonomic constrained systems, which both amply use themodern differential geometry, such as fibre bundle theory, the structureof symplectic and Poisson manifolds. The two kinds of Lagrange theories of geometric dynamics for nonholonomic constrained systems,i.e., the extrinsic and the intrinsic ones, are summarized specially. They include the fundamentalconcepts of jet bundle geometry needed in describing time-dependent mechanical systems,decomposition of jet bundles into a direct sum according to the constraints, horizontal distributions on constraintmainifolds, the global formulation of D'Alembert-Lagrange's equations and Chaplygin's equations, and nonholonomic mechanicson a Riemann-Cartan manifold. Meanwhile, the geometric significance ofChetaev's conditions and $\rd$-$\delta$ commutation relation are discussed in depth. Finally some other important topics,such as Hamiltonian framework and pseudo-Poisson structure, Noether'ssymmetries and Lie's symmetries, momentum maps and reduction theory of nonholonomicmechanics, and Vakonomic dynamics are briefly reviewed.
DYNAMICS OF OVERLAN FLOW AND SOIL EROSION (II) SOIL EROSION
2004, 34(4): 493-506. doi: 10.6052/1000-0992-2004-4-J2002-077
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This paper briefly introduced the basiccharacteristics and main types of soil erosion on hillslopes, and summarizedthe research advances in the dynamic process and prediction model of soilerosion on the hillslopes, including the surface-sealed soils, splasherosion, sheet flow (interrill) erosion, rill erosion, sediment transport ofoverland flow, critical slope gradient of soil erosion, and predictionmodeling of soil erosion. Also, the future trends of soil erosion dynamicsare discussed.
2004, 34(4): 507-528. doi: 10.6052/1000-0992-2004-4-J2004-006
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Understanding the combustion process is essential for the energy utilization in a safe, efficient and clean way. However, in normal gravity, the buoyant convection and gravitational sedimentation make the process complicated. Such effects nearly disappear in microgravity, which will simplify the research on combustion. In view of the combustion process occured on ground and the fire safety problem for manned spacecraft, the research on microgravity combustion involves various fields of combustion science, including premixed gas combustion, gaseous diffusion combustion, droplet combustion, particle combustion, dust combustion and flame spread over fuel surface, during the development of about a half century, especially the last decade. Through the research, the droplet combustion with spherical symmetry, dust combustionwithout sedimentation effect and combustion in quiescent or low speed convection environment have been realized, the flame ball, self-extinguishing flame and other phenomena were observed, and the thermophoresis effect during soot formation, flammability limit and flame instability and other mechanism were clarified. The research has deepened the knowledge of combustion phenomenon and especially deepened the understanding on radiation effect. It is shown that, for premixed gas combustion, gaseous diffusion combustion and droplet combustion, there is also the quenching extinction limit caused by large radiative heat loss, besides the blowoff extinction limit caused by short residence time. The former can be found only under microgravity condition. Some of these results have already been absorbed into the textbook. The fact that the combustion under microgravity shows different characteristics from that under normal gravity is important for fire safety for manned spacecraft. Acounting for the condition of our country and present research advances, the coal particle combustion, the dust combustion, the mechanism related to soot, radiation effect andchemical dynamics would serve as the promising future directions.
ADVANCES IN STRENGTH THEORIES FOR MATERIALS UNDER COMPLEX STRESS STATE IN THE 20TH CENTURY
2004, 34(4): 529-560. doi: 10.6052/1000-0992-2004-4-J2002-054
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It is 100 years since thewell-know Mohr-Coulomb strength theory was established in 1900. Aconsiderable amount of theoretical and experimental research on strengththeory of materials under complex stress state was done in the 20thCentury. This review article presents a survey of the advances instrength theory (yield criteria, failure criterion, etc) of materials(including matellic materials, rock, soil, concrete, ice, iron,polymers, energetic material, etc) under complex stress, discusses therelationship among various criteria, and gives a method of choosing areasonable failure criterion for applications in research andengineering. Three series of strength theories, the unified yieldcriterion, the unified strength theory, and others are summarized. Thisreview article contains 1163 references regarding the strength theories. This review also includes a biref discussion of the computational implementation of the strength theories and multi-axial fatigue.
2004, 34(4): 561-561. doi: 10.6052/1000-0992-2004-4-J2004-123
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2004, 34(4): 562-562. doi: 10.6052/1000-0992-2004-4-J2004-134
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2004, 34(4): 563-563. doi: 10.6052/1000-0992-2004-4-J2004-180
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The supported projects on mechanics of NSFC for 2004
2004, 34(4): 564-564. doi: 10.6052/1000-0992-2004-4-J2004-162
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2004, 34(4): 568-569. doi: 10.6052/1000-0992-2004-4-J2004-168
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2004, 34(4): 579-579. doi: 10.6052/1000-0992-2004-4-J2004-114
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2004, 34(4): 579-579. doi: 10.6052/1000-0992-2004-4-J2004-136
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2004, 34(4): 580-580. doi: 10.6052/1000-0992-2004-4-J2004-118
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2004, 34(4): 581-581. doi: 10.6052/1000-0992-2004-4-J2004-177
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2004, 34(4): 582-582. doi: 10.6052/1000-0992-2004-4-J2004-178
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2004, 34(4): 582-583. doi: 10.6052/1000-0992-2004-4-J2004-179
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2004, 34(4): 584-584. doi: 10.6052/1000-0992-2004-4-J2004-138
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