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  • 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 More >

  • Open Access

    ARTICLE

    A Direct Discrete Formulation of Field Laws: The Cell Method

    Enzo TONTI1

    CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 237-258, 2001, DOI:10.3970/cmes.2001.002.237

    Abstract We present a new numerical method for the solution of field equations. The essence of the method is to directly provide a discrete formulation of field laws, without using and requiring a differential formulation. It is proved that, for linear interpolation, the stiffness matrix so obtained coincides with the one of the Finite Element Method. For quadratic interpolation, however, the present stiffness matrix differs from that of FEM; moreover it is unsymmetric. It is shown that by using a parabolic interpolation, a convergence of the fourth order is obtained. This is greater than the one More >

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