A study was made of the invariant properties of defect potentials that were capable of describing defect motion in a continuum. By formulating two canonical defect theories (generalized Nye, Kröner-de Wit), three defect potentials were found that were variational. That is, their associated Euler-Lagrange equations were differential compatibility conditions on the continuum and defects. Consequently, the symmetry properties of these variational functionals yielded several classes of new conservation law and invariant integral which were related to continuum compatibility conditions that were independent of the constitutive relationships of the continuum. The contour integral of the corresponding conserved quantity was path-independent if the domain encompassed by such an integral was specifically defect-free. The invariant integral was used to study macroscopic brittle fracture, and a so-called multi-scale Griffith criterion was proposed which led to a rigorous justification of the familiar Griffith-Irwin theory.

On Variational Symmetry of Defect Potentials and Multiscale Configurational Force. S.Li: Philosophical Magazine, 2008, 88[7], 1059-84