Improved SNS-PFEM framework with dual mortar method to model geotechnical large deformation contact problems

Abstract

This work proposes an improved stable node-based strain smoothing particle finite element method (SNS-PFEM) with the dual mortar method to model the geotechnical large deformation contact problems. The proposed SNS-PFEM framework requires only basic length parameters for constructing stabilization terms, thus yielding a simpler implementation and less computational cost than the existing methods. Based on this framework, an efficient dual mortar contact algorithm is introduced for finite frictional sliding analysis, utilizing the segment-to-segment discretization and dual Lagrange multiplier method. The resulting stiffness matrix is well-conditioned and positive-defined, leading to higher accuracy and less computational cost than penalty-type methods. Furthermore, a dynamic mesh adjustment technique is proposed to ensure high mesh quality throughout the large deformation process. Since all variables are stored on the node in our SNS-PFEM framework, the process of mesh adjustment is both straightforward and computationally efficient. The precision and robustness of our methods are validated through three classical benchmarks and two representative geotechnical problems. Results show that the proposed SNS-PFEM framework effectively eliminates the over-soft issue seen with the NS-PFEM; the dual mortar method offers an accurate, and efficient performance for nonlinear contact analysis; and the dynamic mesh adjustment technology is effective in preventing mesh quality degradation during large deformations.