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{\bf Submacroscopically Stble Equilibria\\
of Bodies Undergoing\\
Disarrangements and Dissipation} 

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Luca Deseri\\
Department of Mechanical and Structural Engineering\\
Universit\`a di Trento\\
38050 Trento, ITALY

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David R. Owen\\
Department of Mathematical Sciences\\
Carnegie Mellon University\\
Pittsburgh, PA  15213, USA\\
do04@andrew.cmu.edu
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\noindent {\bf Abstract}:  Elasticity is viewed here as a starting point in
the description of inelastic behavior.  The two-scale geometry provided by
structured deformations and a field theory of elastic bodies undergoing
disarrangements (non-smooth geometrical changes) and dissipation are used to
formulate and illustrate a concent of ``submacroscopically stable
configuration.''  A body in a submacroscopically stable equilibrium
configuration resists additional submacroscopic geometrical changes such as
the occurrence of microslips, the formation of microvoids, and the appearance
of localized distortions that, together, leave the macroscopic configuration
of the body unchanged.  Submacroscopically stable configurations represent
energetically preferred phases for the bodies in equilibrium, and a procedure
is described here for determining the submacroscopically stable equilibra of a
body.  The procedure is carried out in detail here for two classes of bodies
that may undergo disarrangements and experience internal dissipation.  One
class is characterized by its bi-quadratic free energy response function, and
the requirement of submacroscopic stability reduces from five to one the
number of phases available to a body that is in equilibrium under mixed
boundary conditions.  For subclass of these bi-quadratic free energy
functions, the distinguished phase determined through this procedure has the
same free energy response as one derived for nematic elastomers via
statistical calculations.  Boundary-value problems for the macroscopic
deformation corresponding to a submacroscopically stable equilibrium in a body
of this class are formulated.  A second class of bodies, the ``near-sighted
fluids,'' has both a prolate and a spherical phase that may occur in
equilibrium; the submacroscopically stable equilibria of a near-sighted fluid
must be stress-free, without regard to the particular phase that appears.  In
all considerationsin this article, the term ``equilibrium'' is synonymous
wiith satisfaction of balance of forces and moments in a given environment.

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