Galerkin-based finite strain analysis with enriched radial basis interpolation

Abstract

We present an enriched radial basis function (RBF) interpolation, which is combined with a symmetric Galerkin method to solve finite strain problems. Specifically, Wendland compact support radial basis functions (RBF) are enriched with a quadratic polynomial, whose parameters are condensed-out during the shape-function construction phase. A total Lagrangian technique is adopted and for finite strain plasticity the formalism with the Mandel stress is adopted. These recent developments are especially convenient from the implementation perspective, as RBF formulations for finite strain plasticity have been limited by interpolation updating. We also note that, although tetrahedra are adopted for quadrature in the undeformed configuration, mesh deformation is of no consequence for the results. Four benchmark tests are successfully solved, with extensive convergence studies and showing clear advantages with respect to finite-element in terms of robustness and with respect to classical Element-Free Galerkin (EFG) formulations in terms of efficiency.