Some Entropy Rate Approaches in Continuum Mechanics

Irreversible processes are accompanied by an increase in the internal entropy of a continuum, and as such the entropy production function is fundamental in determining the overall state of the system. In this talk, it will be shown that the entropy production function can be utilized for a variational analysis of certain dissipative continua in two different ways. Firstly, a novel unified Lagrangian-Hamiltonian formalism is constructed giving phase space extra structure, and applied to the study of fluid flow and brittle fracture.  Secondly, a maximum entropy production principle is presented for simple bodies and its implications to the study of fluid flow discussed.