ABSTRACT
Suppose that in uniaxial tension, the elastic modulus is Ee and the inelastic modulusrelating stress and inelastic strain increments are Ei, and Ei<<Ee. The total uniaxial
modulus is then
19.2 THERMOPLASTICITY
As in Chapter 18, two potential functions are introduced to provide a systematic way to describe irreversible and dissipative effects. The first is interpreted as the Helmholtz freeenergy density, and the second is for dissipative effects. To accommodate kinematic hardening, we also assume an extension of the Green and Naghdi (G-N) (1965) formulation, in which the Helmholtz free energy decomposes into reversible and
irreversible parts, with the irreversible part depending on the “plastic strain.” Here, it also depends on the temperature and a workless internal state variable.
