Subfluids

Abstract

This lecture concerns a class of simple materials ¹ called simple subfluids, or more briefly subfluids. These are simple materials for which the isotropy group contains a dilatation group, i.e., a group of all unimodular pure stretches and reflections in three linearly independent directions . In other words, a dilatation group, h can be indexed by a linearly independent set of three vectors, say {e ₁,e ₂,e ₃}, such that a tensor A ∈ h̳ ⇔ there exist real numbers λ₁ , λ₂ , λ₃ such that

$$\begin{array}{*{20}c} {\,\,\,\,\,\,\,\,\,\,\left| {\lambda _{1\,} \,\lambda _2 \,\lambda _3 } \right| = 1,} & {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\rm{and}}} \\ {{\rm{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{A} \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{e} }}_{\,\,\,{\rm{i}}} \,\lambda _{1\,} \,\,\,{\rm{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{e} }}_{\text{i}} \,} & {{\rm{for}}\,\,\,\,{\rm{i}}\,{\rm{ = }}\,{\rm{1,}}\,{\rm{2,}}\,{\rm{3}}\,\,{\rm{.}}} \\ \end{array} $$