  Strong-form meshless methods received much attention in recent years and are
being extensively researched and applied to a wide range of problems in science
and engineering. However, the solution of elasto-plastic problems has proven to
be elusive because of often non-smooth constitutive relations between stress
and strain. The novelty in tackling them is the introduction of virtual finite
difference stencils to formulate a hybrid radial basis function generated
finite difference (RBF-FD) method, which is used to solve smallstrain von Mises
elasto-plasticity for the first time by this original approach. The paper
further contrasts the new method to two alternative legacy RBF-FD approaches,
which fail when applied to this class of problems. The three approaches differ
in the discretization of the divergence operator found in the balance equation
that acts on the non-smooth stress field. Additionally, an innovative
stabilization technique is employed to stabilize boundary conditions and is
shown to be essential for any of the approaches to converge successfully.
Approaches are assessed on elastic and elasto-plastic benchmarks where
admissible ranges of newly introduced free parameters are studied regarding
stability, accuracy, and convergence rate.
