Formulation of balance relations and configurational fields for continua with microstructure and moving point defects via invariance

Abstract

Abstract The purpose of this work is the formulation of models for the dynamics of continua with microstructure and material inhomogeneity. In particular, attention is focused here on the balance relations and configurational fields for such continua obtained via invariance. To this end, the approach of Capriz (Capriz, G., 1989. Springer Tracts in Natural Philosophy, vol. 37) to the formulation of continua with microstructure as based upon the invariance of the internal power with respect to superimposed rigid-body rotations is extended to one based upon the Euclidean frame-indifference of the total energy balance. This is then combined with an extension of the work of Gurtin (Gurtin, M.E., 1995. Arch. Rat. Mech. Anal. 131, 67–100) on the formulation of static configurational fields to the case of dynamic and microstructure. In this way, one obtains in particular the dependence of the configurational momentum density, configurational or Eshelby stress, as well as the internal and external configurational momentum supply rate, or configurational force, densities, on the corresponding microstructural fields. These can then be used to derive the forms of the balance relations relevant to the case that the continuum contains defects at which the microstructure is discontinuous. As an application of the formulation, this is done here for the case of a continuum with microstructure containing a single defect.