Protection barriers impacted by multiple surges of flow-like landslides: A Material Point Method numerical study

The dual domain material point (DDMP) method is explored as a candidate to be implemented in a general purpose code to perform simulations of materials with complex geometry that undergo large history-dependent deformation and failure. To test its candidacy, we study its mesh convergence, its sensitivity to mesh orientation, and its ability to handle softening and failure of a material. Simulations of large deformation and simulations of mechanical failure are performed using both DDMP and the material point method (MPM). When cell-crossing of material points is not an issue and when there are a sufficient number of material points in each computation cell, the numerical error decreases with the square of the cell size as expected for both MPM and DDMP. DDMP has reduced error compared with MPM when there are many instances of material points crossing cell boundaries due to the continuous nature of the modified gradient of the shape functions. Simulations of a specimen under tension are also performed where the background mesh is aligned and misaligned with the tension direction. MPM displays a significant mesh-dependent stress field, DDMP shows negligible mesh dependency. Despite a mesh orientation-dependent stress field from MPM, the critical tension and failure mode from both MPM and DDMP calculations have negligible mesh dependency when using a non-local failure model. If only the failure mode is important (i.e., local stresses are unimportant), MPM with a non-local failure model is a suitable method for modeling failure with small deformations. However, if local stresses are also important or if there are large deformations with many cell-crossings before failure, DDMP should be the method that is used. A needed improvement for DDMP is identified from our numerical simulations.

The Material Point Method (MPM) uses a combined Eulerian-Lagrangian approach to solve problems involving large deformations. A problem domain is discretised as material points which are advected on a background grid. Problems are encountered with the original MPM when material points cross between grid cells, and this has been tackled by the development of the Generalised Interpolation MPM, where material points’ domains of influence extend beyond the currently occupied grid cell. In this paper, the Generalised Interpolation Material Point (GIMP) Method has been implemented implicitly in a manner that allows a global stiffness matrix to be constructed similar to that in the Finite Element Method (FEM) by combining contributions from individual elements on the background grid. An updated Lagrangian finite deformation framework has been used to ensure non-linear behaviour within each of the loadsteps. The weighting functions used for this which make the GIMP method different to standard MPM are presented and the implementation is explained. Specific details on computing the deformation gradient to be consistent with the updated Lagrangian framework and the updating of the material point influence domains are outlined, both of which are currently unclear in the published literature. It is then shown through numerical examples that for both small and large deformation elastic and elasto-plastic problems, the implicit GIMP method agrees well with analytical solutions and exhibits convergence properties between that of linear and quadratic FEM.

Improved coupling of finite element method with material point method based on a particle-to-surface contact algorithm

Material point method enhanced by modified gradient of shape function

Nodal force error and its reduction for material point methods

<p>The study of landslides spans from pre-failure mechanisms to post-failure propagation. The risk posed by landslides often relies more on the latter, and quantitative analysis for it can also describe the hazard caused by landslides more intuitively. Traditional numerical methods, such as the finite element method (FEM), suffer from severe mesh distortions when dealing with the highly nonlinear problems of landslides, especially in the post-failure propagation, resulting in inefficient or even failed computations. Meshfree methods such as the material point method (MPM) can efficiently describe the large deformation process of a structure using material points by reducing the dependence on the mesh. However, its computational efficiency is much lower compared to FEM. Currently, MPM programs are written in languages like C/C++/Fortran, which are performant but difficult to implement and read, and in languages like MATLAB/Python, which are flexible and easy to read but at the cost of much lower performance. This is known as the “two-language problem”. A new programming language, Julia, recently rose to prominence in scientific computing. It is designed for high-performance computing, has many of the features of advanced programming languages, and solves the "two-language problem". Benefiting from the native support for GPU computing in Julia, we can easily introduce GPU computing in the program to efficiently simulate the dynamic process in the post-failure of landslide. Consequently, for such a computationally intensive task, programming a high-performance MPM in Julia would be an attractive alternative. We use the Generalized Interpolation Material Point (GIMP) method, a variant of MPM, to perform the simulations and demonstrate the capabilities of the Julia language for high-performance scientific computing.</p>

Sand and soil are comprised of large amounts of discrete particles, which may lead to a transition between solid and fluid-like states in large deformation problems. How to deal with the complex transitions between these states in granular media is the key to explaining the run-out of a landslide. The Shenzhen (China) landfill landslide exemplifies a type of large deformation demonstrating this transition between solid and fluid-like states. The soil in the landfill was mainly composed of completely decomposed granite (CDG). The landslide's run-out traveled in fluid-like fashion several hundred meters and caused casualties. In this paper, we use the material point method (MPM) based on the softening model and contact algorithm to analyze the run-out of the Shenzhen landfill landslide. MPM offers substantial advantages in numerical simulations of problems involving extra-large deformations. The latest research of landslide simulations is reviewed, and the fundamental principles of MPM are introduced in the first part of the paper. Then, the post-failure behavior of the large slope in the Shenzhen landfill is simulated with the generalized interpolation material point (GIMP) method with a softening model and a contact algorithm, respectively. The trend of the velocities and displacements of material points are calculated. Topographies of the post-failure landslide using different parameters are analyzed.

Material point methods applied to one-dimensional shock waves and dual domain material point method with sub-points

A FEMP method and its application in modeling dynamic response of reinforced concrete subjected to impact loading

Application of a Second-order Implicit Material Point Method

A generalized interpolation material point method for modelling coupled seepage-erosion-deformation process within unsaturated soils

The material point method (MPM) shows promise for the simulation of large deformations in history-dependent materials such as soils. However, in general, it suffers from oscillations and inaccuracies due to its use of numerical integration and stress recovery at non-ideal locations. The development of a hydro-mechanical model, which does not suffer from oscillations is presented, including a number of benchmarks which prove its accuracy, robustness and numerical convergence. In this study, particular attention has been paid to the formulation of two-phase coupled material point method and the mitigation of volumetric locking caused numerical instability when using low-order finite elements for (nearly) incompressible problems. The numerical results show that the generalized interpolation material point (GIMP) method with selective reduced integration (SRI), patch recovery and composite material point method (CMPM) (named as GC-SRI-patch) is able to capture key processes such as pore pressure build-up and consolidation.KeywordsCoupled behaviorHydro-mechanicalLarge deformationMaterial point methodReduced integrationConsolidation

This study presents the formulation and implementation of a fully implicit stabilised Material Point Method (MPM) for dynamic problems in two-phase porous media. In particular, the proposed method is built on a three-field formulation of the governing conservation laws, which uses solid displacement, pore pressure and fluid displacement as primary variables (u–p–U formulation). Stress oscillations associated with grid-crossing and pore pressure instabilities near the undrained/incompressible limit are mitigated by implementing enhanced shape functions according to the Generalised Interpolation Material Point (GIMP) method, as well as a patch recovery of pore pressures – from background nodes to material points – based on the same Moving Least Square Approximation (MLSA) approach investigated by Zheng et al. [1]. The accuracy and computational convenience of the proposed method are discussed with reference to several poroelastic verification examples, spanning different regimes of material deformation (small versus large) and dynamic motion (slow versus fast). The computational performance of the proposed method in combination with the PARDISO solver for the discrete linear system is also compared to explicit MPM modelling [1] in terms of accuracy, convergence rate, and computation time.

In this paper, we focus on three issues related to applications of material point methods (MPMs) to objects with complex geometries. They are material point generation, compatibility of material points with a mesh, and sensitivity to mesh orientation. An efficient method of generating material points from a stereolithography (STL) file is introduced. This material point generation method is independent of the mesh used in MPM calculations. The compatibility between the material points and the mesh is then studied. We also show that the original MPM and the dual domain material point (DDMP) method are sensitive to mesh orientation. These issues are related to the calculation of the internal force and are concerns of the MPMs. They become more prominent when MPMs are applied to complex geometries. Our numerical results show that the recently developed local stress difference (LSD) algorithm (Perez et al. in J Comp Phys 498:112681, 2024) can be used to effectively address them.

This paper presents a single-point Material Point Method (MPM) for large deformation problems in two-phase porous media such as soils. Many MPM formulations are known to produce numerical oscillations and inaccuracies in the simulated results, largely due to numerical integration and stress recovery performed at non-ideal locations, cell crossing errors, and mass moving from one background grid cell to another. The same drawbacks lead to even worse consequences in the presence of an interstitial fluid phase, especially when undrained/incompressible conditions are approached. In this study, an explicit stabilised MPM, based on the Generalised Interpolation Material Point (GIMP) method with Selective Reduced Integration (SRI), is proposed to mitigate typical numerical oscillations in (nearly) incompressible coupled problems. It includes two additional features to improve stress and pore pressure recovery, namely (i) patch recovery of pore pressure increments based on a Moving Least Squares Approximation, and (ii) two-phase extension of the Composite Material Point Method for effective stress recovery. The combination of components leads to a new method named GC-SRI-patch. After a detailed description of the approach, its effectiveness is verified through analysing various consolidation problems, with emphasis on the representation of pore pressures in time and space.