A three-dimensional continuum theory of dislocation plasticity - Modelling and application to a composite

The increasing demand for materials with well defined microstructure, which is accompanied by the advancing miniaturization of devices calls for physically motivated, dislocation-based continuum theories of plasticity. Only recently rigorous techniques have been developed for performing meaningful averages over systems of moving, curved dislocations, yielding evolution equations for a higher order dislocation density tensor. Our continuum dislocation theory allows for generalizing the planar system towards a three-dimensional system, where dislocations may have arbitrary orientation and curvature. With the inclusion of curvature, the theory naturally takes into account a deformation-induced increase in the overall dislocation density without having to invoke ad-hoc assumptions about dislocation sources. A numerical implementation and some benchmark tests of this continuum theory for dislocation dynamics has already been discussed in the literature. In this paper, we apply this continuum theory to composite materials, where we analyze a plastically deforming matrix with an elastic inclusion.