In the small deformation theory the volumetric strain, Ask an Expert

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In the small deformation theory, the volumetric strain (dV_x - dV₀)/dV₀ is approximated by ε₁₁ + ε₂₂ + ε₃₃, while in the large deformation theory, it is given by J - 1.

Show that when the deformation is small, the latter can be approximated by the former.

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