| A finite element method is developed for dislocations in arbitrary, three-dimensional bodies, including micro-/nano-devices, and layered materials, such as thin films. The method is also compatible with anisotropic materials, and can readily be applied to non-linear media. In this method, dislocation are modeled by adding discontinuities to extend the conventional finite element basis. Two approaches for adding discontinuities to the conventional finite element basis are proposed. In the first, a simple discontinuous enrichment imposes a constant jump in displacement across dislocation glide planes. In the second approach, the enrichments more accurately approximate the dislocations by capture the singular asymptotic behavior near the dislocation core. A basis of singular enrichments are formed from the analytical solutions to straight dislocation lines, but are applicable for more general, curved dislocation configurations. Methods for computing the configurational forces on dislocation lines within the XFEM framework have also been developed. For jump enrichments, an approach based on an energy release rate or J-integral is proposed. When singular enrichments are available, it is shown that the Peach-Koehler equation can be used to compute forces directly. This new approach differs from many existing methods for studying dislocations because it does not rely on superposition of solutions derived analytically or through Green's functions. This extended finite element approach is suitable to study dislocations in micro- and nano-devices, and in specific material micro-structures, where complicated boundaries and material interfaces are pervasive. |
