A general solution to some plane problems of micropolar elasticity

William E. Warren, Esben Byskov

    Research output: Contribution to journalConference article in JournalResearchpeer-review

    10 Citations (Scopus)

    Abstract

    We obtain a general solution to the field equations of plane micropolar elasticity for materials characterized by a hexagonal or equilateral triangular structure. These materials exhibit 3-fold symmetry in the plane and the elastic response is isotropic. Utilizing two displacement potential functions, the solution is obtained in terms of two analytic functions and a third function satisfying the modified homogeneous Helmholtz equation. Expressions for the two-dimensional components of displacement, stress, and couple stress, along with the resultant force on a contour, are presented.We observe that micropolar effects are most significant in material regions subjected to large deformation gradients. Specific results are presented for the classical crack problem, the half plane loaded uniformly on the surface, Flamant's problem, and the circular cylinder compressed by equal and opposite oncentrated forces.
    Original languageEnglish
    JournalEuropean Journal of Mechanics A - Solids
    Volume27
    Issue number1
    Pages (from-to)18-27
    Number of pages10
    ISSN0997-7538
    DOIs
    Publication statusPublished - 2008
    EventThe American Academy of Mechanics Conference - New Orleans, Louisiana, United States
    Duration: 17 Jun 200820 Jun 2008
    Conference number: 1

    Conference

    ConferenceThe American Academy of Mechanics Conference
    Number1
    CountryUnited States
    CityNew Orleans, Louisiana
    Period17/06/200820/06/2008

    Keywords

    • Micropolarity
    • Complex functions
    • Helmholtz equation

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