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  • Open Access

    ARTICLE

    Computer Simulation of Fundamental Behaviors of Point Defects, Clusters and Interaction with Dislocations in Fe and Ni

    E. Kuramoto, K. Ohsawa, T. Tsutsumi1

    CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.2, pp. 193-200, 2002, DOI:10.3970/cmes.2002.003.193

    Abstract In order to investigate the interaction of point defects with a dislocation, an interstitial cluster or a SFT (stacking fault tetrahedron), computer simulation has been carried out in model Fe and Ni crystals. The capture zone (the region where the interaction energy is larger than kT) was determined for various interactions. Calculated capture zone for T =500°C for SIAs (crowdion and dumbbell) around a straight edge dislocation is larger than that for a vacancy in both Fe and Ni. Capture zones for Ni are larger than those for Fe, suggesting that Ni (fcc) has a larger dislocation bias factor than… More >

  • Open Access

    ARTICLE

    A Variational Multiscale Method to Embed Micromechanical Surface Laws in the Macromechanical Continuum Formulation

    K. Garikipati1

    CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.2, pp. 175-184, 2002, DOI:10.3970/cmes.2002.003.175

    Abstract The embedding of micromechanical models in the macromechanical formulation of continuum solid mechanics can be treated by a variational multiscale method. A scale separation is introduced on the displacement field into coarse and fine scale components. The fine scale displacement is governed by the desired micromechanical model. Working within the variational framework, the fine scale displacement field is eliminated by expressing it in terms of the coarse scale displacement and the remaining fields in the problem. The resulting macromechanical formulation is posed solely in terms of the coarse scale displacements, but is influenced by the fine scale; thereby it has… More >

  • Open Access

    REVIEW

    The Emerging Role of Multiscale Modeling in Nano- and Micro-mechanics of Materials

    Nasr M. Ghoniem1, Kyeongjae Cho2

    CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.2, pp. 147-174, 2002, DOI:10.3970/cmes.2002.003.147

    Abstract As a result of surging interest in finding fundamental descriptions for the strength and failure properties of materials, and the exciting prospects of designing materials from their atomic level, an international symposium on Multiscale Modeling was convened at ICES'2K in Los Angeles during August 23 - 25, 2000. In this symposium, 23 speakers with research interests spanning fields as diverse as traditional mechanics, physics, chemistry and materials science have given talks at this symposium. The topics of discussion were focused on sub-continuum modeling of the mechanics of materials, taking into account the atomic structure of solid materials. The main motivation… More >

  • Open Access

    ARTICLE

    Generation-Phase Simulation of Dynamic Crack Bifurcation Phenomenon Using Moving Finite Element Method Based on Delaunay Automatic Triangulation

    T. Nishioka1, J. Furutuka1, S. Tchouikov1, T. Fujimoto1

    CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.1, pp. 129-146, 2002, DOI:10.3970/cmes.2002.003.129

    Abstract The governing condition of dynamic crack bifurcation phenomena had not been fully elucidated until our recent experimental studies. We found from the experimental results that the energy flux per unit time into a propagating crack tip or into a fracture process zone governs the crack bifurcation. Regarding the numerical simulation of dynamic crack bifurcation, to the authors' knowledge, no accurate simulations have been carried out, due to several unresolved difficulties. In order to overcome the difficulties, for the analysis of dynamic crack bifurcation, we developed a moving finite element method based on Delaunay automatic triangulation. Using the moving finite element… More >

  • Open Access

    ARTICLE

    Meshless BEM for Three-dimensional Stokes Flows

    C.C. Tsai1, D.L. Young2, A.H.-D. Cheng3

    CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.1, pp. 117-128, 2002, DOI:10.3970/cmes.2002.003.117

    Abstract This paper describes a combination of the dual reciprocity method (DRM) and the method of fundamental solution (MFS) as a meshless BEM (DRM-MFS) to solve three-dimensional Stokes flow problems by the velocity-vorticity formulation, where the DRM is based on the compactly supported, positive definite radial basis functions (CS-PD-RBF). In the velocity-vorticity formulation, both of the diffusion type vorticity equations and the Poisson type velocity equations are solved by DRM-MFS. Here a typical internal cubic cavity flow and an external flow past a sphere are presented. The results are acceptable. Furthermore, this paper provides a preliminary work for applications to the… More >

  • Open Access

    ARTICLE

    Nodal Constraint, Shear Deformation and Continuity Effects Related to the Modeling of Debonding of Laminates, Using Plate Elements

    E. H. Glaessgen1, W.T. Riddell2, I. S. Raju1

    CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.1, pp. 103-116, 2002, DOI:10.3970/cmes.2002.003.103

    Abstract The effects of several critical assumptions and parameters on the computation of strain energy release rates for delamination and debond configurations modeled with plate elements have been quantified. The method of calculation is based on the virtual crack closure technique (VCCT), and models of the upper and lower surface of the delamination or debond that use two-dimensional (2D) plate elements rather than three-dimensional (3D) solid elements. The major advantages of the plate element modeling technique are a smaller model size and simpler configurational modeling. Specific issues that are discussed include: constraint of translational degrees of freedom, rotational degrees of freedom… More >

  • Open Access

    ARTICLE

    A dimensional reduction of the Stokes problem

    Olivier Ricou1, Michel Bercovier2

    CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.1, pp. 87-102, 2002, DOI:10.3970/cmes.2002.003.087

    Abstract In this article, we present a method of reduction of the dimension of the Stokes equations by one in a quasi-cylindrical domain. It takes the special shape of the domain into account by the use of a projection onto a space of polynomials defined over the thickness. The polynomials are defined to fit as well as possible with the variables they approximate. Hence, this method restricted to the first polynomial, recovers the Hele-Shaw approximation.
    The convergence of the approximate solution to the continuous one is shown. Under a regularity hypothesis, we also obtain error estimates.
    A description of… More >

  • Open Access

    ARTICLE

    A Micromechanical Theory of Flow in Pulmonary Alveolar Sheet

    Z. Zhong1, Y. Dai1,2, C. C. Mei3, P. Tong1,4

    CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.1, pp. 77-86, 2002, DOI:10.3970/cmes.2002.003.077

    Abstract In this paper we reexamine the sheet-flow model proposed by Fung and Sobin (1969) for blood flow in capillaries in the pulmonary alveoli from micromechanical point of view. The pulmonary alveolar capillary is assumed to be two parallel membranes connected by periodic tissue posts. Blood is spread out into the very thin layer or sheet between the two membranes. The pulmonary alveolar sheet thus has a microstructure of hexagonal cells. A two-scale theory of homogenization is used to establish the canonical equations for the unit cell. The microscale solution is obtained by means of finite element method and the macroscopic… More >

  • Open Access

    ARTICLE

    On a Meshfree Method for Singular Problems

    Weimin Han, Xueping Meng1

    CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.1, pp. 65-76, 2002, DOI:10.3970/cmes.2002.003.065

    Abstract Interests in meshfree (or meshless) methods have grown rapidly in the recent years in solving boundary value problems arising in mechanics, especially in dealing with difficult problems involving large deformation, moving discontinuities, etc. Rigorous error estimates of a meshfree method, the reproducing kernel particle method, for smooth solutions have been theoretically derived and experimentally tested in Han, Meng (2001). In this paper, we provide an error analysis of the meshfree method for solving problems with singular solutions. The results are presented in the context of one-dimensional problems. The error estimates are of optimal order and are supported by numerical results. More >

  • Open Access

    ARTICLE

    A Meshless Local Petrov-Galerkin Method for Solving the Bending Problem of a Thin Plate

    Shuyao Long1, S. N. Atluri2

    CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.1, pp. 53-64, 2002, DOI:10.3970/cmes.2002.003.053

    Abstract Meshless methods have been extensively popularized in literature in recent years, due to their flexibility in solving boundary value problems. The meshless local Petrov-Galerkin(MLPG) method for solving the bending problem of the thin plate is presented and discussed in the present paper. The method uses the moving least-squares approximation to interpolate the solution variables, and employs a local symmetric weak form. The present method is a truly meshless one as it does not need a mesh, either for the purpose of interpolation of the solution or for the integration of the energy. All integrals can be easily evaluated over regularly… More >

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