• Research paper •

### Invariant tensor function representations of constitutive equations for the isotropic and rate independent materials

• Received:2007-03-29 Revised:2008-01-04 Online:2008-09-25 Published:2008-09-25

Abstract: This paper combines the internal variable theory and the tensor function representation theory to establish the constitutive equations of the deformation theory and the increment theory for the isotropic and rate independent materials. In the equations, there are three complete and irreducible base tensors, that is, the stress tensor of the zero order, the first order and the second order power, to show that the principal axes of plastic strain and its increment are coincident with those of the stresses. With the orthogonalization of the base tensors, the geometrical explanation of the constitutive equations is obtained in the principal stress space. Furthermore, the coefficients in the constitutive equations of deformation theory (or increment theory) can be derived with three invariants of stresses and plastic strain ( or plastic strain increments). Meanwhile, the present constitutive equations may reduce to classical deformation theory (or plastic potential theory), and be consistent to the singular yield surface theory.