The volumetric strain, also called bulk strain, is the relative variation of the volume, as arising from dilation or compression ; it is the first strain invariant or trace of the tensor: δ δ = Δ Δ V V 0 = I 1 = ε ε 11 + ε ε 22 + ε ε 33 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 a ⋅ ⋅ ( 1 + ε ε 11 ) × × a ⋅ ⋅ ( 1 + ε ε 22 ) × × a ⋅ ⋅ ( 1 + ε ε 33 ) and V 0 = a, thus Δ Δ V V 0 = ( 1 + ε ε 11 + ε ε 22 + ε ε 33 + ε ε 11 ⋅ ⋅ ε ε 22 + ε ε 11 ⋅ ⋅ ε ε 33 + ε ε 22 ⋅ ⋅ ε ε 33 + ε ε 11 ⋅ ⋅ ε ε 22 ⋅ ⋅ ε ε 33 ) ⋅ ⋅ a 3 − − a 3 a 3 as we consider small deformations, 1 ≫ ≫ ε ε i i ≫ ≫ ε ε i i ⋅ ⋅ ε ε j j ≫ ≫ ε ε 11 ⋅ ⋅ ε ε 22 ⋅ ⋅ ε ε 33 therefore the formula.