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Remarks on material frame-indifference controversy

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Abstract

Regarding a frame of reference as an observer, the notion of frame-indifference (also referred to as objectivity) concerns the transformation properties of physical quantities under change of observer. For kinematic quantities, they can usually be derived from the deformation/motion, while for non-kinematic quantities, such as force and stress, A frame-indifference property must be postulated. frame-indifference postulate for the stress, sometimes unsuitably called the principle of frame-indifference, is a universal assumption, which has nothing to do with material properties. This has caused some confusions in the interpretation of “material” frame-indifference in the literature. Material frame-indifference deals with the constitutive functions, which characterize intrinsic properties of the material under different observers. We shall carefully render these concepts mathematically and deduce the well-known condition of material objectivity as a consequence of the frame-indifference postulate and the principle of material frame-indifference. We shall also emphasize and remark on some persistent controversy and some misleading statements found in recent literature.

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Authors and Affiliations

  1. Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil

    I-Shih Liu

  2. Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, Brazil

    Rubens Sampaio

Authors
  1. I-Shih Liu
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  2. Rubens Sampaio
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Correspondence to I-Shih Liu.

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Liu, IS., Sampaio, R. Remarks on material frame-indifference controversy. Acta Mech 225, 331–348 (2014). https://doi.org/10.1007/s00707-013-0973-4

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  • DOI: https://doi.org/10.1007/s00707-013-0973-4

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