A Discontinuous Galerkin Method for an Incompatibility-Based Strain Gradient Plasticity Theory
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 wordsinterior penalty lifting operator microforces
Unable to display preview. Download preview PDF.
- 1.G. Engel, K. Garikipati, T.J.R. Hughes, M.G. Larson, L. Mazzei, R.L. Taylor. Continuous/discontinuous finite element approximations of fourth-order elliptic problems in structural and continuum mechanics with application to thin beams and plates, and strain gradient elasticity. Computer Methods in Applied Mechanics and Engineering 191, 3669–3750, 2002.MATHCrossRefMathSciNetGoogle Scholar
- 6.L. Noels, R. Radovitzky. An explicit discontinuous Galerkin method for non-linear solid dynamics: Formulation, parallel implementation and scalability properties. International Journal for Numerical Methods in Engineering, DOI: 10.1002/nme.2213.Google Scholar