  This paper deals with a numerical analysis of plastic deformation under
various conditions, utilizing Radial Basis Function (RBF) approximation. The
focus is on the elasto-plastic von Mises problem under plane-strain assumption.
Elastic deformation is modelled using the Navier-Cauchy equation. In regions
where the von Mises stress surpasses the yield stress, corrections are applied
locally through a return mapping algorithm. The non-linear deformation problem
in the plastic domain is solved using the Picard iteration.
  The solutions for the Navier-Cauchy equation are computed using the Radial
Basis Function-Generated Finite Differences (RBF-FD) meshless method using only
scattered nodes in a strong form. Verification of the method is performed
through the analysis of an internally pressurized thick-walled cylinder
subjected to varying loading conditions. These conditions induce states of
elastic expansion, perfectly-plastic yielding, and plastic yielding with linear
hardening. The results are benchmarked against analytical solutions and
traditional Finite Element Method (FEM) solutions. The paper also showcases the
robustness of this approach by solving case of thick-walled cylinder with
cut-outs. The results affirm that the RBF-FD method produces results comparable
to those obtained through FEM, while offering substantial benefits in managing
complex geometries without the necessity for conventional meshing, along with
other benefits of meshless methods.
