A Note on the Objectivity (Rotational Invariance) of the Stored Energy Density in Continuum Physics

Jiashi Yang

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arXiv · 2409.07478

A Note on the Objectivity (Rotational Invariance) of the Stored Energy Density in Continuum Physics

Jiashi Yang

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Abstract

This short note is concerned with the rotational invariance of the stored energy density in continuum physics as a scalar function of a few vectors. A simple derivation is presented for the determination of the general form of the energy density in the case of a two-dimensional space. It is also shown that the general form of the energy density so determined may be further reduced. The three-dimensional case is also discussed.

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Jiashi Yang. 2024-08-31. A Note on the Objectivity (Rotational Invariance) of the Stored Energy Density in Continuum Physics. https://arxiv.org/abs/2409.07478

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