A nonequilibrium thermodynamic theory of viscoplastic materials

A nonequilibrium thermodynamic theory for predicting the mechanical behavior of materials beyond the elastic range is formulated. The theory incorporates the idea of a ‘‘concealed’’ parameter α, originally due to Bridgman [Rev. Mod. Phys. 22, 56 (1950)], where the constitutive equations are governed by (a) a thermodynamic potential such as a generalized Gibbs function, G, or Helmholtz free-energy function, F, each with an explicit dependence on α, and (b) a prescription for α̇, the time rate of change of α, such that α̇ is directly proportional to the negative of Gα or Fα, the partial derivative of G or F with respect to α, respectively. The theory is found to be consistent with (1) the second law of thermodynamics regarding entropy production; (2) the concept of Lyapunov stability at equilibrium; (3) the rule of invariance with respect to a transformation of parameters; and (4) the powerful law of invariance with respect to the Legendre transformation. Significance of the new formulation is discussed by solving a class of one-dimensional creep and fatigue modeling problems and by comparing the new theory with several similar approaches in the literature.