Hybrid natural element method for large deformation elastoplasticity problems

We present the hybrid natural element method (HNEM) for two-dimensional elastoplastic large deformation problems. Sibson interpolation is adopted to construct the shape functions of nodal incremental displacements and incremental stresses. The incremental form of Hellinger-Reissner variational principle for elastoplastic large deformation problems is deduced to obtain the equation system. The total Lagrangian formulation is used to describe the discrete equation system. Compared with the natural element method (NEM), the HNEM has higher computational precision and efficiency in solving elastoplastic large deformation problems. Some numerical examples are selected to demonstrate the advantage of the HNEM for large deformation elastoplasticity problems.