On the Mathematical Modeling of Entropy Producing Processes
                        Distinguished Professor
                  Forsyth Chair in Mechanical Engineering
                        Professor of Mathematics
                      Professor of Biomedical Engineering
                       Professor of Civil Engineering
           Senior Research Scientist, Texas Transportation Institute


        In this talk, a general thermodynamic approach will be presented
for modeling a class of material responses that has as its basis the
notion that during a process that the material is subject to, the
"natural configuration" from which the response of the body is described
can change: the evolution of the "natural configurations" being
determined by a certain thermodynamic criterion. 
          The body can also have different material symmetries with
regard to these different natural configurations and this allows one to
model processes during which the symmetry of the body changes. We
consider bodies that can be described by a family of non-dissipative
responses characterized by stored energy functions parameterized from an
evolving set of "natural configurations".  The evolution of the "natural
configurations" is accompanied by dissipation and entropy production.
The way in which the natural configurations change is determined by the
maximization of "entropy production".  By choosing different forms for
the stored energy, rate of dissipation, etc., we can capture different
types of dissipative responses as that evidenced in: classical
plasticity, twinning, solid to solid phase transition, deformation of
multi-network polymers, response of viscoelastic bodies, crystallization
in polymers, flows of liquid crystals, the response of geological
materials, growth and adaptation of biological materials, etc.  The body
possessing different natural configurations leads naturally to ideas
introduced by Eshelby concerning configurational forces. The
thermodynamic setting also provides a natural setting for generalizing
the reciprocal relations due to Onsager.