On Hill’s lemma in continuum mechanics

François Nicot, Nicolaas P. Kruyt, Olivier Millet

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    7 Citations (Scopus)
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    Hill’s first-order lemma in continuum mechanics has been derived in the literature for quasi-static cases and for dynamic cases in the absence of body forces. In this manuscript, a generalized first-order Hill identity is first derived in an Eulerian dynamic description including body forces. Then, a second-order Hill identity using a Lagrangian description is obtained, involving the variation in time of the associated kinetic energy. Simple examples, that allow for analytical analysis, of one-dimensional elastic deformation of bars are considered that involve dynamics and body forces to illustrate the generalization of Hill’s identities proposed here.
    Original languageEnglish
    Pages (from-to)1581-1596
    JournalActa mechanica
    Issue number5
    Publication statusPublished - 2017


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