Extending the transport theorem to rough domains of integration

Brian Seguin, Denis F. Hinz, Eliot Fried

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    Transport theorems, such as that named after Reynolds, are an important tool in the field of continuum physics. Recently, Seguin and Fried used Harrison's theory of differential chains to establish a transport theorem valid for evolving domains that may become irregular. Evolving irregular domains occur in many different physical settings, such as phase transitions or fracture. Here, emphasizing concepts over technicalities, we present Harrison's theory of differential chains and the results of Seguin and Fried in a way meant to be accessible to researchers in continuum physics. We also show how the transport theorem applies to three concrete examples and approximate the resulting terms numerically. Furthermore, we discuss how the transport theorem might be used to weaken certain basic assumptions underlying the description of continua and the challenges associated with doing so.
    Original languageEnglish
    Article number050802
    Number of pages16
    JournalApplied Mechanics Reviews
    Volume66
    Issue number5
    DOIs
    Publication statusPublished - Sep 2014

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