Editing Infinitesimal strain theory (section)

===Volumetric strain===
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The '''volumetric strain''', also called '''bulk strain''', is the relative variation of the volume, as arising from ''[[dilation (physics)|dilation]]'' or ''compression''; it is the [[#Strain invariants|first strain invariant]] or [[trace (matrix)|trace]] of the tensor:
<math display="block">\delta=\frac{\Delta V}{V_0} = I_1 = \varepsilon_{11} + \varepsilon_{22} + \varepsilon_{33}</math>
Actually, if we consider a cube with an edge length ''a'', it is a quasi-cube after the deformation (the variations of the angles do not change the volume) with the dimensions <math>a \cdot (1 + \varepsilon_{11}) \times a \cdot (1 + \varepsilon_{22}) \times a \cdot (1 + \varepsilon_{33})</math> and ''V''<sub>0</sub> = ''a''<sup>3</sup>, thus
<math display="block">\frac{\Delta V}{V_0} = \frac{\left ( 1 + \varepsilon_{11} + \varepsilon_{22} + \varepsilon_{33} + \varepsilon_{11} \cdot \varepsilon_{22} + \varepsilon_{11} \cdot \varepsilon_{33}+ \varepsilon_{22} \cdot \varepsilon_{33} + \varepsilon_{11} \cdot \varepsilon_{22} \cdot \varepsilon_{33} \right ) \cdot a^3 - a^3}{a^3}</math>
as we consider small deformations,
<math display="block">1 \gg \varepsilon_{ii} \gg \varepsilon_{ii} \cdot \varepsilon_{jj} \gg \varepsilon_{11} \cdot \varepsilon_{22} \cdot \varepsilon_{33} </math>
therefore the formula.

[[Image:Approximation volume deformation.png|class=skin-invert-image|400px|<small>Real variation of volume  (top) and the approximated one (bottom): the green drawing shows the estimated volume and the orange drawing the neglected volume</small>]]

In case of pure shear, we can see that there is no change of the volume.