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Why is the zero divergence of displacement field means that a body's volume is conserved?

I got this question while reading the research paper "ON THE DERIVATION OF ELECTRIC BODY FORCE,COUPLE AND POWER IN AN ELECTROELASTIC BODY" Author: Jiashi Yang

In the paper the author assumes that the infinitesimal displacement field preserves the volume of the electronic continuum (which is a continuum that is massless and having a negative charge density), and after that he writes that the divergence of infinitesimal displacement field is equal to zero.

user134613
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  • Are you asking about the divergence theorem? If the divergence of the displacements is zero, there is no source or sink of volume. – Chemomechanics Dec 14 '22 at 20:39
  • Yes. But how is the divergence of displacement related to change of volume? What is the proof that the divergence of displacement is equal to source or sink of volume – user134613 Dec 14 '22 at 20:45
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    You can search online for divergence "displacement field" volume conservation as well as I can. The first hit I get is here; see specifically the discussion following Eq. (1.22). – Chemomechanics Dec 14 '22 at 21:10
  • Sorry for my delay. I read the part you mentioned. And it's the right answer. Thank you. – user134613 Jan 01 '23 at 08:53
  • It mentions that volumetric strain is equal to the divergence of displacement. Thus zero divergence of displacement implies that volume is conserved. – user134613 Jan 01 '23 at 08:54

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Volumetric strain is equal to the divergence of displacement. Thus zero divergence of displacement implies that volume is conserved.

user134613
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