A thermodynamic theory of localized deformation based on the operator principle

The dissipation field of a continuum is studied here by a new operator theory of irreversible thermodynamics; the evolution equations of the dissipation field can be obtained in the condition of knowing the phenomenological nonlinear constitutive relation of materials. In this theory, the basic state equation, which is the state of minimum dissipation, is utilized for solving the distribution of the dissipation field of quasi-statics, and the higher order state equations are corresponding to the dissipation fields of dynamics. The paper also gives a method to get the dissipation force operator by using Helmholtz’s free energy function. In the final part of this paper, several important phenomena of the localized deformation, such as the plastic instability of necking and shear band, are predicted in the form of an analytical formula.