u‐p semi‐Lagrangian reproducing kernel formulation for landslide modeling

Abstract

This paper presents a u-p (displacement-pressure) semi-Lagrangian reproducing kernel (RK) formulation to effectively analyze landslide processes. The semi-Lagrangian RK approximation is constructed based on Lagrangian discretization points with fixed kernel supports in the current configuration. As a result, it tracks state variables at discretization points while allowing extreme deformation and material separation that is beyond the capability of Lagrangian formulations. The u-p formulation following Biot theory is incorporated into the formulation to describe poromechanics of saturated geomaterials.In addition, a stabilized nodal integration method to ensure stability of the domain integration and kernel contact algorithms to model contact between bodies are introduced in the u-p semi-Lagrangian RK formulation. The proposed method is verified with several numerical examples and validated with an experimental result and the field data of an actual landslide.

Circumventing volumetric locking in stabilized smoothed particle finite element method and its application to dynamic large deformation problems

“…It is associated with the under‐integration property of the nodal integration since too few integration points produce a rank‐deficiency in the stiffness matrix and lead to a spurious numerical oscillation in dynamic problems. This rank‐deficiency caused by the under‐integration in nodal integration has also been found in many other particle‐based mesh‐free methods 31–34 . Since nodal integration plays a core role in SPFEM, such a rank‐deficiency can also bother the SPFEM.…”

“…This rankdeficiency caused by the under-integration in nodal integration has also been found in many other particle-based mesh-free methods. [31][32][33][34] Since nodal integration plays a core role in SPFEM, such a rank-deficiency can also bother the SPFEM. To circumvent the rank-deficiency associated with nodal integration, several stabilized approaches have been developed.…”

“…In the least-squares method, artificial penalty parameters are needed for the stabilization. (2) The stress points stabilization method, 31,33,36,37 in which stability is achieved by adding additional stress points. In the stress points stabilization method, the computational cost has dramatically increased because the number of additional stabilization stress points is almost equal to the initial particle number.…”

A hardening/softening viscoplastic model for large deformation of soil

“…For more diffuse responses, other methods are more appropriate, such as finite element method with Lagrangian Integration Points (FEMLIP). 25,26 A host of meshfree methods, such as element-free Galerkin, 27,28 smoothed-particle hydrodynamics, [29][30][31][32] and the reproducing kernel particle method [33][34][35] have been developed explicitly for large-deformation analysis and applied to problems in soil mechanics. In this paper, we use standard finite elements and leave the integration with numerical methods for very large deformations for future investigation.…”

Simulation of debris flow on an instrumented test slope using an updated Lagrangian continuum particle method

“…Over the years, theoretical models and computational simulation tools have been developed for modeling debris flows [30,44,66]. As noted earlier, continuum-based particle methods such as the material point method [5,27,64], reproducing kernel particle method [23,56], peridynamics [34], and the smoothed particle hydrodynamics [16-19, 22, 28, 29, 32, 37, 38, 45-49, 74] are preferable techniques because they can accommodate very large deformations and do not suffer from severe mesh distortion. Discrete element methods (DEM) share the same desirable features [20,24,31,33,54,67,68,72]; however, they lack scalability to problems larger than laboratory sizes.…”