Murdoch, A.I. (2006) Some primitive concepts in continuum mechanics regarded in terms of space-time molecular averaging: the key role played by inertial observers. Journal of Elasticity, 84 (1). pp. 69-97. ISSN 0374-3535Full text not available in this repository. (Request a copy from the Strathclyde author)
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, Physics, Mechanics of Materials, Materials Science(all), Mechanical Engineering|
|Subjects:||Science > Physics|
|Department:||Faculty of Science > Mathematics and Statistics > Mathematics|
|Depositing user:||Strathprints Administrator|
|Date Deposited:||06 Dec 2006|
|Last modified:||06 Jan 2017 03:53|