0
REVIEW ARTICLES

A Review of Material Frame-Indifference in Mechanics

[+] Author and Article Information
Charles G. Speziale

Aerospace and Mechanical Engineering Department, Boston University, Boston, MA 02215

Appl. Mech. Rev 51(8), 489-504 (Aug 01, 1998) (16 pages) doi:10.1115/1.3099017 History: Online April 20, 2009

Abstract

The Principle of Material Frame-Indifference in various areas of mechanics is critically reviewed from a basic theoretical standpoint. Modern continuum mechanics is considered along with statistical mechanics and turbulence in an effort to better understand this commonly used axiom. It is argued that Material Frame-Indifference is a restricted invariance that can be highly useful in the formulation of constitutive equations but must be applied with caution. Material Frame-Indifference applies, in a strong approximate sense, to most areas of continuum mechanics where there is a clear cut separation of scales so that the ratio of fluctuating to mean time scales is extremely small. While it breaks down for the three-dimensional case, it rigorously applies to Reynolds stress models in the limit of two-dimensional turbulence where an analogy is made between the Reynolds stress tensor and the non-Newtonian part of the stress tensor in the laminar flow of a non-Newtonian fluid. On the other hand, the general invariance group of constitutive equations that is universally valid is the extended Galilean group of transformations which includes arbitrary time-dependent translations of the spatial frame of reference; rotational frame-dependence then enters exclusively through the intrinsic spin tensor. In order to definitively address this issue it is necessary to establish what the invariance group is of solutions to the fluctuation dynamics from which constitutive equations are formally constructed. The implications of these results for future research in a variety of different fields in mechanics are thoroughly discussed. This article includes 52 references.

Copyright © 1998 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In