Towards an unconditionally stable numerical scheme for continuum dislocation transport

Hector Alonso Hernandez Velazquez, T. J. Massart, R. H. J. Peerlings, M. G. D. Geers

Research output: Contribution to journalArticleAcademicpeer-review

5 Citations (Scopus)
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Recent developments in plasticity modeling for crystalline materials are based on dislocations transport models, formulated for computational efficiency in terms of their densities. This leads to sets of coupled partial differential equations in a continuum description involving diffusion and convection-like processes combined with non-linearity. The properties of these equations cause the most traditional numerical methods to fail when applied to solve them. Therefore, dedicated stabilization techniques must be developed in order to obtain physically meaningful and numerically stable approximations. The objective of this paper is to present a dedicated stabilization technique and to apply it to a system of dislocation transport equations in one dimension. This stabilization technique, based on coefficient perturbations, successfully provides unconditional stability with respect to the spatial discretization. Several of its favorable characteristics are discussed, providing evidence of its versatility and effectiveness through a thorough numerical assessment.
Original languageEnglish
Article number085013
Pages (from-to)1-24
JournalModelling and Simulation in Materials Science and Engineering
Issue number8
Publication statusPublished - Dec 2015


  • crystal plasticity
  • dislocation transport
  • stabilized finite element method


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