A note on the accurate expression of strain tensor;

The influences of deformation and Poisson ratio on the volume ratio under different strain tensor descriptions are studied.

The expressions of the Lagrangian-Green strain tensor and the Eulerian strain tensor and their work-conjugate stress tensors,namely,the second Piola-Kirchhoff stress tensor and Cauchy stress tensor,are derived for the beam under axial uniformly tension,and the constitutive relations of these two pairs of work-conjugate stress and strain measures are also presented.

Firstly transforms Cartesian coordinates of stress tensor,which in Navier-Stokes equation,to spherical coordinate,then does vector transform of spherical coordinate to Navier-Stokes equation.

Comparing with these viscoelastic strain increment expressions,it is concluded that for linear viscoelastic model,if the viscoelastic deformation law under different stress states,such as stress tensor,deviation stress and bulk stress,are the same,their parameters yield as Ek/ηk=Gsk/ηsk=Kmk/ηmk.

Based on the theory of matrix, this paper focuses on the similarity of stress tensor in different coordinate systems and then an instance performed by Ansys and Matlab is given to validate this conclusion.