Slip-induced conservation laws for dislocation structures in the finite kinematic framework

In the present paper we develop a general framework that captures topological, geometric, and energetic aspects of slip surfaces to provide conservation laws for dislocation structures. In this work, dislocations act as the boundary of active slip regions that support a finite displacement jump, while treating the material outside the slip regions with a continuum mechanic framework in the setting of large deformations. Within this semicontinuous description, it is shown that the condition of slip imposes an important restriction on the shape of the slip surfaces regardless of the material structure. This catalog of shapes for the slip surfaces can be further restricted for crystalline materials, providing a simple geometric description of common dislocation processes such as cross slip or dislocation loop glide. In this setting, the classical Kirchhoff-type rule for the conservation of the Burgers vector emanates directly from the formulation, while recent conservation laws designed for partial dislocations in face centered cubic crystals are also naturally captured.