Comparative study of face-based smoothed point interpolation method and linear finite element method for elastoplastic and large deformation problems in geomaterials

Nonlinear deformation of geomaterials is one of the important problems in geotechnical engineering. Compared with the finite element method (FEM), meshfree face-based smoothed point interpolation method (FSPIM) has a more exact stiffness and low mesh dependence, which shows great potential in simulating the nonlinear deformation of geomaterials. Compared with the linear FEM, this paper studies the calculation accuracy and efficiency of FSPIM with the T4 scheme for elastoplastic and large deformation problems in geomaterials. This paper first derives the elastoplastic and large deformation SPIM, including the smoothing deformation gradient, smoothing Green–Lagrange strain, the discrete updated Lagrangian governing equation, and elastoplastic constitutive relations that eliminate the effects of rigid body motion. Then, two effective analysis programs are developed for comparative analysis based on the FSPIM and linear FEM. Two classical slope models with different geometrical parameters and constitutive models are employed for numerical tests. Based on the numerical test results, the performance of FSPIM in the analysis of elastoplastic and large deformation problems in geomaterials is evaluated by comparing it with the linear FEM. Finally, the simulation results are discussed, and future work of the FSPIM is proposed.