An adaptive interpolation material point method and its application on large-deformation geotechnical problems

A novel Material Point Method (MPM) called the Adaptive Interpolation Material Point Method (AIMPM) is proposed to simulate large deformation problems in this work. The proposed method combines the domain interpolation proposed by the Convected Particle Domain Interpolation (CPDI) with the particle interpolation from the original MPM to address large deformation problems of geotechnical materials. The novelty of the model is twofold. First, the 3D domain interpolation formula is extended, and the volume term in the shape function is calculated from the corner points characterizing the material configuration. Second, the particle interpolation and the domain interpolation are coupled to accurately reflect the stress-strain behavior of geotechnical materials under large deformation. The two interpolation methods can be transformed adaptively through the criterion of Jacobian determinant or equivalent plastic strain. The performance of the AIMPM is verified by axial vibration, generalized vortex, rectangular collision, and column collapse cases. The simulation results show that the AIMPM significantly reduces the cell crossing error by domain interpolation compared to the MPM. More importantly, AIMPM is more accurate in capturing the exact location of geotechnical material flow. The work described in this study demonstrates the capability of the AIMPM in simulations of large deformation geotechnical problems.