Finite element implementation and numerical issues of strain gradient plasticity with application to metal matrix composites

Per Frederiksson, Peter Gudmundson, Lars Pilgaard Mikkelsen

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    Abstract

    A framework of finite element equations for strain gradient plasticity is presented. The theoretical framework requires plastic strain degrees of freedom in addition to displacements and a plane strain version is implemented into a commercial finite element code. A couple of different elements of quadrilateral type are examined and a few numerical issues are addressed related to these elements as well as to strain gradient plasticity theories in general. Numerical results are presented for an idealized cell model of a metal matrix composite under shear loading. It is shown that strengthening due to fiber size is captured but strengthening due to fiber shape is not. A few modelling aspects of this problem are discussed as well. An analytic solution is also presented which illustrates similarities to other theories.
    Original languageEnglish
    JournalInternational Journal of Solids and Structures
    Volume46
    Issue number22-23
    Pages (from-to)3977-3987
    ISSN0020-7683
    DOIs
    Publication statusPublished - 2009

    Keywords

    • Materials research
    • Light strong materials for wind turbines and for transportation

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