A stabilized, symmetric Nitsche method for spatially localized plasticity
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A heterogeneous interface method is developed for combining primal displacement and mixed displacement-pressure formulations across nonconforming finite element meshes to treat volume-preserving plastic flow. When the zone of inelastic response is localized within a larger domain, significant computational savings can be achieved by confining the mixed formulation solely to the localized region. The method’s distinguishing feature is that the coupling terms for joining dissimilar element types are derived from a time-discrete free energy functional, which is based on a Lagrange multiplier formulation of the interface constraints. Incorporating residual-based stabilizing terms at the interface enables the condensation of the multiplier field, leading to a symmetric Nitsche formulation in which the interface operators respect the differing character of the governing equations in each region. In a series of numerical problems, the heterogeneous interface method achieved comparable results on coarser meshes as those obtained from applying the mixed formulation throughout the domain.
KeywordsJ2-plasticity Nitsche method Discontinuous Galerkin Variational Multiscale method Mixed formulation