### Abstract

Original language | English |
---|---|

Pages (from-to) | 69-97 |

Number of pages | 28 |

Journal | Journal of Elasticity |

Volume | 84 |

Issue number | 1 |

DOIs | |

Publication status | Published - 29 Mar 2006 |

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### Keywords

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

### Cite this

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**Some primitive concepts in continuum mechanics regarded in terms of space-time molecular averaging: the key role played by inertial observers.** / Murdoch, A.I.

Research output: Contribution to journal › Article

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 -