Nitsche-based material point method for large deformation frictional contact problems

Large deformation problems in practical engineering are often accompanied by contact phenomena. While the conventional material point method (MPM) is efficient at solving large deformation problems, it cannot handle slip contacts. This paper presents Nitsche’s method for analysing large deformations with frictional contact via the MPM. Nitsche’s method has good features of variational consistency and no additional unknowns, and it is integrated into the MPM in a weak manner based on the principle of virtual power. Within the integrated formulation, both biased and unbiased computational schemes are derived to adapt to different forms of contact. Additionally, B-spline shape functions are employed to alleviate cell-crossing noise, and an improved particle extrapolation approach for accurate contact detection is introduced. The efficacy of the proposed Nitsche-based MPM is validated through several representative benchmarks from the literature. We further apply the proposed method to simulate the water leakage problem of the lining gasketed joint in shield tunnels. Comparison with experimental results demonstrates the applicability of the proposed method.