Abstract:

The author presents the general invariant formulation of constitutive equations based on the representation theorem for the isotropic materials. The equations are a linear combination of three irreducible tensor function bases, which depend on the zero, first and second order power of stress tensor and are orthogonal to one another. Three coefficients depend on three invariants of stresses and plastic strain increments respectively. The internal variables are defined in terms of three invariants of the plastic strain increments. Therefore, the evolution equations of the internal variables are needed to be determined to form a closed constitutive theory. Using the representation theorem, the evolution equations are obtained in a general form. It depends on the increment of invariants of the stress, and therefore is independent of the rotation of the principal axes of stress. It is discussed how the evolution equations are specified from the experiment data in combination with some assumptions. Finally, the constitutive equations presented in this paper are compared with the classical plastic potential theory and the multi-yield surface theory. It is showed that the former is a general representation of the latter two theories, and is more simple and convenient for use.

Key words: internal variable, tensor function representation theorem, constitutive equations, plastic potential, isotropy, yield surface