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Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Singularityfree dislocation dynamics with strain gradient elasticity
 Journal of the Mechanics and Physics of Solids 68 (2014), pp.161178 ISSN: 00225096 
 Deutsche Forschungsgemeinschaft DFG La1974/21 
 Deutsche Forschungsgemeinschaft DFG La1974/22 
 Deutsche Forschungsgemeinschaft DFG La1974/31 

 English 
 Journal Article 
 Fraunhofer IWM () 
Abstract
The singular nature of the elastic fields produced by dislocations presents conceptual challenges and computational difficulties in the implementation of discrete dislocationbased models of plasticity. In the context of classical elasticity, attempts to regularize the elastic fields of discrete dislocations encounter intrinsic difficulties. On the other hand, in gradient elasticity, the issue of singularity can be removed at the outset and smooth elastic fields of dislocations are available. In this work we consider theoretical and numerical aspects of the nonsingular theory of discrete dislocation loops in gradient elasticity of Helmholtz type, with interest in its applications to three dimensional dislocation dynamics (DD) simulations. The gradient solution is developed and compared to its singular and nonsingular counterparts in classical elasticity using the unified framework of eigenstrain theory. The fundamental equations of curved dislocation theory are given as nonsingular line integrals suitable for numerical implementation using fast onedimensional quadrature. These include expressions for the interaction energy between two dislocation loops and the line integral form of the generalized solid angle associated with dislocations having a spread core. The single characteristic length scale of Helmholtz elasticity is determined from independent molecular statics (MS) calculations. The gradient solution is implemented numerically within our variational formulation of DD, with several examples illustrating the viability of the nonsingular solution. The displacement field around a dislocation loop is shown to be smooth, and the loop selfenergy nondivergent, as expected from atomic configurations of crystalline materials. The loop nucleation energy barrier and its dependence on the applied shear stress are computed and shown to be in good agreement with atomistic calculations. DD simulations of LomerCottrell junctions in Al show that the strength of the junction and its configuration are easily obtained, without adhoc regularization of the singular fields. Numerical convergence studies related to the implementation of the nonsingular theory in DD are presented.