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The complete and irreducible representation of tensor function, contains a non-linear constitutive equation of general and coordinated invariance form, and rules for the number and type of the introduction scalar variables, and has also been clear about the independent elastic and elasto-plastic tensor forms. In addition, the material of symmetry (voigt symmetry, isotropic, anisotropy, crystal symmetry, etc.) limits the tensor form in the constitutive relation, and rules for the numbers of independent components in elastic and elasto-plastic tensor functions. On the basis of the symmetry, the numbers of 2n order independent elastic constants and elastic-plastic constants of isotropic, anisotropic, orthotropic materials are derived. It will lay the foundation for further research on elasto-plastic constitutive equations which are complete and irreducible for isotropic, anisotropic, orthotropic materials.

Elastic and Elasto-plastic Constants in Non-linear Constitutive Equation