A centroid-enriched strain-smoothed radial point interpolation method for nearly incompressible elastoplastic problems in solid mechanics

While edge-based (2D) and face-based (3D) smoothed radial point interpolation methods (ES-RPIM and FS-RPIM) have demonstrated excellent performance in solid mechanics, the volumetric locking problem limits their applications in nearly incompressible problems. This paper develops a centroid-enriched edge-based/face-based smoothed RPIM (CE-ES-RPIM and CE-FS-RPIM) to address the volumetric locking problem in nearly incompressible problems. The proposed method comprises the following elements: (1) a centroid-enriched scheme is creatively used and implemented into the traditional ES-RPIM and FS-RPIM framework, in which the centroids of triangular mesh are added as spatial discretization nodes; (2) the strain-smoothing technique is performed on triangle (2D) or tetrahedron (3D) mesh to maintain the linear exactness of the radial point interpolation method; and (3) the combination of the centroid-enriched scheme and strain smoothing technique makes the ratio of the number of displacement equations to the number of incompressible constraints reach the optimal value of 2, effectively eliminating volumetric locking. The accuracy, effectiveness and efficiency of the proposed method are validated on several 2D and 3D nearly incompressible benchmark examples. All results demonstrate that the proposed method can provide accurate numerical results under an incompressible limitation and provide better performance than conventional quadratic element methods.