Strain measures, integrability condition and frame indifference in the theory of oriented media

This paper is concerned with the appropriate choice of state variables within the continuum model or oriented media. It is shown that residual deformation, strain and wryness can be considered as such quantities. The compatibility conditions for them are derived, which make the inverse problem of determining the displacement and director triad fields well-posed. The principle of frame indifference justifies the use of these quantities as state variables in the free energy density. Governing and constitutive equations are studied in detail. A comparison with the continuum model of crystals with continuously distributed dislocations is provided. © 1997 Elsevier Science Ltd.