Finite element analysis of discrete edge dislocations: configurational forces and conserved integrals

We present a finite element description of Volterra dislocations using a thermal analogue and the integral representation of dislocations through stresses in the context of linear elasticity. Several analytical results are fully recovered for two dimensional edge dislocations. The full fields are reproduced for edge dislocations in isotropic and anisotropic bodies and for different configurations. Problems with dislocations in infinite medium, near free surfaces or bimaterial interfaces are studied. The efficiency of the proposed method is examined in more complex problems such as interactions of dislocations with inclusions, cracks, and multiple dislocation problems. The configurational (Peach-Koehler) force of the dislocations is calculated numerically based on energy considerations (Parks method). Some important integral conservation laws of elastostatics are considered and the connection between the material forces and the conserved integrals (J and M) is presented. The variable core model of Lubarda and Markenscoff is introduced to model the dislocation core area that is indeterminate by the classical theory.