Analysis of large deformation geotechnical problems using implicit generalized interpolation material point method

This paper presents a quasi-static implicit generalized interpolation material point method (iGIMP) with B-bar approach for large deformation geotechnical problems. The iGIMP algorithm is an extension of the implicit material point method (iMPM). The global stiffness matrix is formed explicitly and the Newton-Raphson iterative method is used to solve the equilibrium equations. Where possible, the implementation procedure closely follows standard finite element method (FEM) approaches to allow easy conversion of other FEM codes. The generalized interpolation function is assigned to eliminate the inherent cell crossing noise within conventional MPM. For the first time, the B-bar approach is used to overcome volumetric locking in standard GIMP method for near-incompressible non-linear geomechanics. The proposed iGIMP was tested and compared with iMPM and analytical solutions via a 1D column compression problem. Results highlighted the superiority of the iGIMP approach in reducing stress oscillations, thereby improving computational accuracy. Then, elasto-plastic slope stabilities and rigid footing problems were considered, further illustrating the ability of the proposed method to overcome volumetric locking due to incompressibility. Results showed that the proposed iGIMP with B-bar approach can be used to simulate geotechnical problems with large deformations.