Most physical models describing fluid flow rely on the
assumption that the Cauchy stress is an explicit function of the
symmetric part of the
velocity gradient of the fluid. This assumption leads to the
Navier-Stokes equations
and its nonlinear generalizations, such as various
electrorheological flow models.
It is known however that the
framework of classical
continuum mechanics, built upon the notions of current and
reference configuration
and an explicit constitutive equation for the Cauchy stress
is too narrow to enable
one to model inelastic behavior of solid-like materials
or viscoelastic properties
of materials. The focus of this minisymposium is
therefore a generalization of the
classical framework of continuum mechanics, called implicit
constitutive theory,
which was proposed recently in a series of papers by Rajagopal.
The underlying principle of implicit
constitutive theory in the
context of viscous flows is the following: instead of demanding
that the Cauchy
stress is an explicit function of the symmetric part of the
velocity gradient, one may
allow an implicit and not necessarily continuous relationship
between these quantities.
The second half of the minisymposion focuses on limiting strain models in elasticity theory involving implicit relations between the Cauchy stress and the strain,
where the linearized strain tensor is a bounded function of the Cauchy stress.