Some primitive concepts in continuum mechanics regarded in terms of space-time molecular averaging: the key role played by inertial observers

    Research output: Contribution to journalArticle

    9 Citations (Scopus)

    Abstract

    In Continuum Mechanics the notions of body, material point, and motion, are primitive. Here these concepts are derived for any (possibly time-dependent) material system via mass and momentum densities whose values are local spacetime averages of molecular quantities. The averaging procedure necessary to ensure molecular-based densities can be agreed upon by all observers (that is, are objective) has implications for constitutive relations. Specifically, such relations should first be expressed in terms of Galilean-invariant functions of the motion relative to an inertial frame. Thereafter such relations can be re-phrased for general observers, thereby yielding general-frame constitutive relations compatible with material frame-indifference. Two postulates concerning observer agreement (which together constitute a statement of material frame-indifference) are shown to imply that any stress response function which is assumed to depend upon the motion in an inertial (general) frame must be Galilean-invariant (invariant under superposed rigid body motions). Accordingly, invariance under superposed rigid body motions is not a fundamental tenet of continuum physics, but rather a consequence of material frame-indifference whenever constitutive dependence upon motion in a general observer frame is postulated.
    Original languageEnglish
    Pages (from-to)69-97
    Number of pages28
    JournalJournal of Elasticity
    Volume84
    Issue number1
    DOIs
    Publication statusPublished - 29 Mar 2006

    Fingerprint

    Continuum mechanics
    Invariance
    Momentum
    Physics

    Keywords

    • material point
    • motion
    • spacetime molecular averaging
    • objectivity
    • material frame-indifference
    • inertial observers
    • continuum mechanics
    • physics

    Cite this

    @article{8c0217f75f0b49cdab32fc45f529d96d,
    title = "Some primitive concepts in continuum mechanics regarded in terms of space-time molecular averaging: the key role played by inertial observers",
    abstract = "In Continuum Mechanics the notions of body, material point, and motion, are primitive. Here these concepts are derived for any (possibly time-dependent) material system via mass and momentum densities whose values are local spacetime averages of molecular quantities. The averaging procedure necessary to ensure molecular-based densities can be agreed upon by all observers (that is, are objective) has implications for constitutive relations. Specifically, such relations should first be expressed in terms of Galilean-invariant functions of the motion relative to an inertial frame. Thereafter such relations can be re-phrased for general observers, thereby yielding general-frame constitutive relations compatible with material frame-indifference. Two postulates concerning observer agreement (which together constitute a statement of material frame-indifference) are shown to imply that any stress response function which is assumed to depend upon the motion in an inertial (general) frame must be Galilean-invariant (invariant under superposed rigid body motions). Accordingly, invariance under superposed rigid body motions is not a fundamental tenet of continuum physics, but rather a consequence of material frame-indifference whenever constitutive dependence upon motion in a general observer frame is postulated.",
    keywords = "material point, motion, spacetime molecular averaging, objectivity, material frame-indifference, inertial observers, continuum mechanics, physics",
    author = "A.I. Murdoch",
    year = "2006",
    month = "3",
    day = "29",
    doi = "10.1007/s10659-005-9048-7",
    language = "English",
    volume = "84",
    pages = "69--97",
    journal = "Journal of Elasticity",
    issn = "0374-3535",
    number = "1",

    }

    TY - JOUR

    T1 - Some primitive concepts in continuum mechanics regarded in terms of space-time molecular averaging: the key role played by inertial observers

    AU - Murdoch, A.I.

    PY - 2006/3/29

    Y1 - 2006/3/29

    N2 - In Continuum Mechanics the notions of body, material point, and motion, are primitive. Here these concepts are derived for any (possibly time-dependent) material system via mass and momentum densities whose values are local spacetime averages of molecular quantities. The averaging procedure necessary to ensure molecular-based densities can be agreed upon by all observers (that is, are objective) has implications for constitutive relations. Specifically, such relations should first be expressed in terms of Galilean-invariant functions of the motion relative to an inertial frame. Thereafter such relations can be re-phrased for general observers, thereby yielding general-frame constitutive relations compatible with material frame-indifference. Two postulates concerning observer agreement (which together constitute a statement of material frame-indifference) are shown to imply that any stress response function which is assumed to depend upon the motion in an inertial (general) frame must be Galilean-invariant (invariant under superposed rigid body motions). Accordingly, invariance under superposed rigid body motions is not a fundamental tenet of continuum physics, but rather a consequence of material frame-indifference whenever constitutive dependence upon motion in a general observer frame is postulated.

    AB - In Continuum Mechanics the notions of body, material point, and motion, are primitive. Here these concepts are derived for any (possibly time-dependent) material system via mass and momentum densities whose values are local spacetime averages of molecular quantities. The averaging procedure necessary to ensure molecular-based densities can be agreed upon by all observers (that is, are objective) has implications for constitutive relations. Specifically, such relations should first be expressed in terms of Galilean-invariant functions of the motion relative to an inertial frame. Thereafter such relations can be re-phrased for general observers, thereby yielding general-frame constitutive relations compatible with material frame-indifference. Two postulates concerning observer agreement (which together constitute a statement of material frame-indifference) are shown to imply that any stress response function which is assumed to depend upon the motion in an inertial (general) frame must be Galilean-invariant (invariant under superposed rigid body motions). Accordingly, invariance under superposed rigid body motions is not a fundamental tenet of continuum physics, but rather a consequence of material frame-indifference whenever constitutive dependence upon motion in a general observer frame is postulated.

    KW - material point

    KW - motion

    KW - spacetime molecular averaging

    KW - objectivity

    KW - material frame-indifference

    KW - inertial observers

    KW - continuum mechanics

    KW - physics

    UR - http://dx.doi.org/10.1007/s10659-005-9048-7

    U2 - 10.1007/s10659-005-9048-7

    DO - 10.1007/s10659-005-9048-7

    M3 - Article

    VL - 84

    SP - 69

    EP - 97

    JO - Journal of Elasticity

    JF - Journal of Elasticity

    SN - 0374-3535

    IS - 1

    ER -