Abstract
The dissipation field of a nonlinear continuum is studied by a new operational theory of irreversible thermodynamics, the evolution equations of the dissipation field can be obtained under the condition of knowing the phenomenological nonlinear constitutive relation of the continuum. In this theory, the dissipation equation of the basic state, which is corresponding to the minimum dissipation principle, is utilized to solve the distribution of dissipation field regarding the equilibrium problem of quasi-statics, and the dissipation equations of higher order are directly related to the dynamics of dissipation fields. The paper also presents a method showing the dissipation force operator by using Helmholtz's free energy function. This paper will also show important phenomena of the localized deformation, such as the plastic instability of necking and shear band, which are predicted in the form of an analytical formula.
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