A linearly conforming point interpolation method (LC-PIM) for perfect Visco-Elastoplastic analysis of 2D solids

Abstract

A linearly conforming point interpolation method (LC-PIM) was recently proposed for the solid mechanics problems. In this paper, the LC-PIM is further extended to perfect visco-elastoplastic analyses of 2D solids. A dual formulation for the LC-PIM with displacements and stresses as the main variables is performed. The von-Mises yield function and the Prandtl-Reuss flow rule are used. In the numerical procedure, however, the stress variables are eliminated and the problem becomes only displacementdependent. The numerical results show that the LC-PIM is much more accurate than the FEM and possesses the upper bound property which is very meaningful for the viscoelastoplastic analyses which almost have not got the analytical solutions. This suggests that we can use two models, LC-PIM and FEM, to bound the solution, and can even estimate the global relative error of numerical solutions.

Keywords

• numerical methods
• mesh-free methods
• linearly conforming point interpolation method (lc-pim)
• upper bound
• visco-elastoplastic analyses.