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A Discontinuous Galerkin Method for an Incompatibility-Based Strain Gradient Plasticity Theory

  • J. Ostien
  • K. Garikipati
Part of the IUTAM BookSeries book series (IUTAMBOOK, volume 11)

Abstract

We consider a recent strain gradient plasticity theory based on incompatibility of plastic strain due to the nature of lattice distortion around a dislocation (J. Mech. Phys. Solids, 52, 2545–2568, 2004). The key features of this theory are an explicit treatment of the Burgers vector, a microforce balance that leads to a classical yield condition, and the inclusion of dissipation from plastic spin. The flow rule involves gradients of the plastic strain, and is therefore a partial differential equation. We apply recently-developed ideas on discontinuous Galerkin finite element methods to treat this higher-order nature of the yield condition, while retaining considerable flexibility in the mathematical space from which the plastic strain is drawn. In particular, despite the higher-order continuity apparent in the yield condition, it is possible to use plastic strain interpolations that are discontinuous across element edges. Two distinct approaches are outlined: the Interior Penalty Method and the Lifting Operator Method. The numerical implementation of the Interior Penalty Method is discussed, and a numerical example is presented.

Key words

interior penalty lifting operator microforces 

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Copyright information

© Springer Science+Business Media B.V 2008

Authors and Affiliations

  • J. Ostien
    • 1
  • K. Garikipati
    • 2
  1. 1.Department of Mechanical EngineeringUniversity of MichiganAnn ArborUSA
  2. 2.Department of Mechanical Engineering & Michigan Center for Theoretical PhysicsUniversity of MichiganAnn ArborUSA

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