Material Point Method Research Articles

A general two-stage initialization for sag-free deformable simulations

Initializing simulations of deformable objects involves setting the rest state of all internal forces at the rest shape of the object. However, often times the rest shape is not explicitly provided. In its absence, it is common to initialize by treating the given initial shape as the rest shape. This leads to sagging, the undesirable deformation under gravity as soon as the simulation begins. Prior solutions to sagging are limited to specific simulation systems and material models, most of them cannot handle frictional contact, and they require solving expensive global nonlinear optimization problems. We introduce a novel solution to the sagging problem that can be applied to a variety of simulation systems and materials. The key feature of our approach is that we avoid solving a global nonlinear optimization problem by performing the initialization in two stages. First, we use a global linear optimization for static equilibrium. Any nonlinearity of the material definition is handled in the local stage, which solves many small local problems efficiently and in parallel. Notably, our method can properly handle frictional contact orders of magnitude faster than prior work. We show that our approach can be applied to various simulation systems by presenting examples with mass-spring systems, cloth simulations, the finite element method, the material point method, and position-based dynamics.

Mechanism of Co‐Seismic Deformation of the Slow‐Moving La Sorbella Landslide in Italy Revealed by MPM Analysis

AbstractPredicting the seismic behavior of slow‐moving landslides presents a significant challenge. Their yearly displacements of a few millimeters to several meters indicate that even before any earthquake they are balancing at the verge of instability. It is therefore not surprising that conventional analysis predicts large co‐seismic displacements even for light‐to‐moderate ground motions. In reality, however, negligibly small displacements have often been observed for such earthquakes, while strong ground motions can still lead to catastrophic failure. This discrepancy challenges both our understanding of the underlying mechanisms and the reliability of conventional analysis, resulting in significant uncertainties for risk assessment. Progress in this field has been further hindered by incompleteness of the available monitoring data and a lack of reliable numerical models capable of dealing simultaneously with small and large deformations under seismic loading. In this article, recently published monitoring data on La Sorbella landslide in Italy and the latest developments in seismic material point method analysis are used to gain insights into the mechanisms controlling the co‐seismic behavior of slow‐moving landslides. This forms the basis for a subsequent investigation of the potential landslide behavior during strong motions, using various material models. The study demonstrates that the co‐seismic behavior of La Sorbella slide is strongly influenced by the interplay between geometrical and viscous effects, as well as potential softening in the shear zone and the surrounding soil mass. The proposed approach paves a way toward quantification of these effects in risk assessment for slow‐moving landslides.

Evaluation of the Material Point Method in Modeling the Post-failure and Run-Out of Translational Landslide: A Case Study in Taiwan

Abstract The material point method (MPM) is an extended finite element method used to simulate large deformation scenarios. A massive translational landslide in Taiwan was adopted to validate the numerical technique for thorough investigations, including the digital terrain models (DTMs), laboratory experiments, and numerical analyses were available in a forensic report. The MPM code Anura3D was used to mimic the landslide’s kinematics, post-failure, and run-out process. An unstable sandstone/shale interlayer was found to lead to the slope sliding; therefore, the before-and-after DTMs from the report mentioned above were used to examine the run-out distance and deposition to determine the best fit for reduced material properties for this layer. The sliding paths, displacements, deviatoric strains, and the velocities of the sliding can be evaluated by dividing the material points into several groups to differentiate the kinematics among them. Meanwhile, the landslide duration and possible maximum safety distance were also assessed. This study has demonstrated that the MPM can analyze the large deformation, post-failure, and run-out distance of landslides. The critical timing of a slope failure is possible to be an essential index on national spatial planning for future disaster reduction.

The power particle-in-cell method

This paper introduces a new weighting scheme for particle-grid transfers that generates hybrid Lagrangian/Eulerian fluid simulations with uniform particle distributions and precise volume control. At its core, our approach reformulates the construction of Power Particles [de Goes et al. 2015] by computing volume-constrained density kernels. We employ these optimized kernels as particle domains within the Generalized Interpolation Material Point method (GIMP) in order to incorporate Power Particles into the Particle-In-Cell framework, hence the name the Power Particle-In-Cell method. We address the construction of volume-constrained density kernels as a regularized optimal transportation problem and describe an iterative solver based on localized Gaussian convolutions that leads to a significant performance speedup compared to [de Goes et al. 2015]. We also present novel extensions for handling free surfaces and solid obstacles that bypass the need for cell clipping and ghost particles. We demonstrate the advantages of our transfer weights by improving hybrid schemes for fluid simulation such as the Fluid Implicit Particle (FLIP) method and the Affine Particle-In-Cell (APIC) method with volume preservation and robustness to varying particle-per-cell ratio, while retaining low numerical dissipation, conserving linear and angular momenta, and avoiding particle reseeding or post-process relaxations.

Post-failure analysis of landslides in spatially varying soil deposits using stochastic material point method

Post-failure analysis of landslides in spatially varying soil deposits using stochastic material point method

Multiscale modeling of coupled thermo-mechanical behavior of granular media in large deformation and flow

Heat generation and transfer in a granular material can be intricately coupled with their mechanical responses, playing a key role in causing excessive large deformation, flow and failure of the material. The coupling may manifest in various forms, including thermal induced stress, mechanically induced heat and thermally induced melting in granular media. We propose a novel hierarchical multiscale modeling framework, TM-DEMPM, to model the coupled thermo-mechanical behavior in granular media which may undergo large deformation and flow. Material Point Method (MPM) is hierarchically coupled with Discrete Element Method (DEM) to offer physics-based, natural scale-crossing simulations of thermo-mechanical granular responses without assuming complicated phenomenological constitutive models. To offer speedup for the numerical solution, hybrid OpenMP and GPU-based parallelization is proposed to take advantage of the hierarchical computing structure of the framework. The proposed framework may provide an effective and efficient pathway to next-generation simulation of engineering-scale large-deformation problems that involve complicated thermo-mechanical coupling in granular media.

Different erosion and entrainment mechanisms in snow avalanches

Erosion significantly affects the dynamics of gravity-driven mass flows. In snow avalanches, the snow cover can be substantially eroded but only partially entrained, however, there are very limited investigations to substantiate this difference. Here, we study various erosion and entrainment behaviors in snow avalanches using the material point method (MPM), finite strain elastoplasticity and critical state soil mechanics. With varied snow properties, distinct erosion patterns are obtained and analyzed with the mass change rate. When there is significant eroded and entrained mass, properties of released snow and erodible bed snow have clear correlations with the eroded mass, but not with the entrained mass, disclosing the difference in erosion and entrainment. Both enhanced and inhibited avalanche mobilities due to erosion and entrainment are captured under different conditions of snow properties and lengths of release and erodible zones. These new insights may stimulate the development of advanced erosion and entrainment models for large-scale avalanches.

Efficient evaluation of run-out distance of slope failure under excavation

The run-out distance (RoD) of slope failure is an important indicator for the quantitative risk assessment of landslides. In recent studies, many attempts have been made to estimate RoD by numerical methods for large deformation analyses (e.g., material point method (MPM)). In spite of the research works, the geotechnical profession is slow to adopt the large deformation analyses to geotechnical design, mainly due to the complex modelling process and large computational effort in the numerical methods. To enable the efficient evaluation of RoD in practice, this note proposes a chart method, referring to the idea of Taylor's stability chart, and focusing on the slopes under excavation. The RoD design charts are established based on the results obtained by MPM, where various slope toe excavation distances are incorporated. The accuracy of the chart method is checked through numerical analyses, and it is found that the proposed chart method can produce accurate RoD estimates with the advantage of efficient computation. The results of this study reveal that the idea of the chart method can be a way to facilitate the application of large deformation analyses in geotechnical design.

Generalization of anisotropic damage mechanics modeling in the material point method

AbstractAnisotropic damage mechanics is derived by redefining its fourth‐ranked damage tensor, , not by its effect on stiffness reduction, but as a tensor that partitions total strain into bulk material strain and an cracking strain associated with crack‐opening displacement. This recharacterization of is irrelevant for 1D modeling, but significantly clarifies 3D algorithms. The new 3D derivation starts with three damage parameters associated with three independent strength models for three components of crack traction. By postulating a traction failure surface dependent on current damage state and requiring that all traction components simultaneously decay to zero at failure, the three damage parameters naturally couple to a single parameter. Many prior methods assume evolving strength depends only on damage. In real materials, strength often depends on other variables such as temperature, pressure, strain rate, and so forth. This article proposes a new general theory that extends prior methods to properly account for such external variables. The general damage mechanics methods must account for extra variables during damage initiation, damage evolution, and elastic loading and unloading. Several examples focus on the new concepts for coupling damage parameters and for using general methods to model materials with pressure‐dependent strength properties.

Efficient cloth simulation based on the material point method

AbstractIn this article, we propose a novel cloth simulation method based on the material point method (abbr. MPM). The response to the cloth strain is characterized by three separated models: the continuous in‐plane hyperelasticity, the discrete bending elastoplasticity, and the continuous frictional contact elastoplasticity. We make use of the moving least squares MPM (abbr. MLS‐MPM) transfer scheme and a discrete bending model to reduce computation overhead. We further extend the hyperelastic bending model to be elastoplastic, which can be further used for the simulation of a wide range of thin shell materials, such as thin metal sheets. A fast and approximate signed distance field generation method for humanoid animation is also proposed. Experimental results demonstrate that our method can efficiently and robustly simulate high‐resolution challenging scenes with hundreds of thousands of triangles.

Relating cone penetration resistance to sand state using the material point method

Cone penetration tests (CPTs) can quantitatively inform about the mechanical state of a sand. However, relating measured cone resistance values to sand state requires complex back-analysis of the processes occurring in the soil during the test. This paper provides new evidence of the value added in this area by modern large-deformation modelling based on the material point method (MPM). It is shown that accurate simulation of the relationship between cone resistance and sand state can be achieved, on condition that the constitutive behaviour of the soil – and especially its critical state features – is adequately modelled over a wide range of confining pressures. This study relies on the predictive capabilities of the critical state NorSand model, and shows how previous calibrations endeavours from the literature (based on triaxial test results) can support the MPM simulation of unrelated CPT results obtained through calibration chamber tests. MPM CPT simulations of ever-increasing quality will positively impact the state of the art of CPT interpretation procedures, to date still largely based on simplified cavity expansion theories.

An immersed MMALE material point method for FSI problems with structure fracturing

The fluid–structure-interaction (FSI) modeling is important for both academic studies and engineering applications, but is also one of the grand challenges in the numerical modeling community. The FSI problems with multi-material fluid flow and extreme structure deformation accompanied with fractures and crack growth are less explored areas. In these problems, the interface reconstruction, multi-material advection, interface interaction on the complicated fluid structure interface and potential structure fragmentation must be all taken into account. This paper aims to present an effective monolithic approach of immersed multi-material arbitrary Lagrangian Eulerian material point method (IALEMPM) by immersing the MPM particles in the MMALE grid. In this novel method, the interfaces between the fluid and structure are tracked implicitly by the MPM particles and the interface interactions are implicitly implemented by assembling the nodal force and the nodal momentum from both the solid particles and fluid cells. The consistence time integration scheme, rezoning phase and remapping phase are also established to guarantee the consistence requirements during the whole simulation. Numerical examples, including a shock-obstacle interaction, a blast-plate interaction and a structure fragmentation are studied by using the IALEMPM, and all the numerical results show good agreement with the benchmark and the experiment data, which indicates that the IALEMPM is effective for solving these complicated FSI problems.

A particle-based parallel scheme for material point method (MPM) using message passing interface (MPI)

A particle-based parallel scheme for material point method (MPM) using message passing interface (MPI)

Multiphysics coupling material point method for modelling frost heave of rock slope

Frost heave is a complex multiphysics coupling problem, and the use of numerical methods to solve such coupling problems has been an increasingly popular research area. The material point method (MPM) is a novel particle-based method combining the advantages of both the Lagrangian and Eulerian approaches, with high potential for application in multiphysics coupling problems. However, compared with other methods, the development of MPM in the field of multiphysics coupling is still inadequate. In order to expands the application of traditional MPM, the proposed multiphysics coupling MPM utilized two sets of material points to discretise the porous medium, also utilized two sets of heat transfer equations to describe heat conduction in the respective fluid and solid, as well as the heat transfer between them. The phase transition was considered using the apparent heat capacity method, and was coupled with other physical fields based on the phase fraction function. The feasibility of the proposed method was verified by comparing with the results of finite element method in five coupling cases. Finally, the proposed method was applied to modelling the frost heave of a rock slope, the distribution of the freezing zone and the mechanism of the frost heaving force were studied.

Post-failure process and kinematic behavior of two landslides: Case study and material point analyses

This paper presents a comprehensive and well-documented landslide case study involving detailed site investigation, field tests, seismic signal analyses, and advanced numerical analyses using the material point method (MPM) to investigate the post-failure process and kinematic behavior of two landslides. The slope failures were triggered by Typhoon Jangmi in September 2008 and had impacts on the downslope residential areas. The background information of two landslides, including geological and hydrological conditions obtained from the detailed site investigation and field tests, was first introduced. The MPM analyses were then conducted and validated by comparing measured and predicted results for the final landslide profiles and duration. The numerical results, including variations in deviatoric strain, volumetric strain, and excess pore water pressure with time, were further examined to determine the post-failure mechanism of the landslides. The effects of soil drainage conditions during landslides on the final landslide profile were also compared and discussed. This study demonstrated that MPM analyses could accurately predict the runout distance of both landslides. The numerical results indicate that the landslides occurred through a complex process of soil failure that involved the stages of shearing, translational movement, compression, and deposition. When the soil was subjected to different loading conditions in different stages, the corresponding post-failure mechanisms are also different. High positive excess porewater pressure could develop near the sliding surface and has a significant influence on landslide kinematics and final landslide profiles. Compared with undrained analysis, fully coupled analysis, which permitted porewater pressure dissipation during a landslide event, produced more accurate predictions of landslide kinematics.

An Efficient B-Spline Lagrangian/Eulerian Method for Compressible Flow, Shock Waves, and Fracturing Solids

This study presents a new method for modeling the interaction between compressible flow, shock waves, and deformable structures, emphasizing destructive dynamics. Extending advances in time-splitting compressible flow and the Material Point Methods (MPM), we develop a hybrid Eulerian and Lagrangian/Eulerian scheme for monolithic flow-structure interactions. We adopt the second-order WENO scheme to advance the continuity equation. To stably resolve deforming boundaries with sub-cell particles, we propose a blending treatment of reflective and passable boundary conditions inspired by the theory of porous media. The strongly coupled velocity-pressure system is discretized with a new mixed-order finite element formulation employing B-spline shape functions. Shock wave propagation, temperature/density-induced buoyancy effects, and topology changes in solids are unitedly captured.

Fully implicit, stabilised MPM simulation of large-deformation problems in two-phase elastoplastic geomaterials

The Material Point Method (MPM) has been gaining increasing popularity as an appropriate approach to the solution of coupled hydro-mechanical problems involving large deformations. This study extends the implicit GIMP-patch method for coupled poroelastic problems recently proposed by Zheng et al. (2021b) to tackle large-deformation problems in (nearly) isochoric elastoplastic geomaterials, particularly by remedying the numerical inaccuracies caused by volumetric locking, such as spurious stress oscillations and an excessively stiff overall response of the system at hand. To overcome these difficulties in two-phase coupled analyses, the B¯ approach of Hughes (1980) is incorporated into an existing version of the implicit GIMP-patch method. Details regarding the formulation and implementation of the proposed method are provided, while several benchmark problems are numerically analysed to evaluate its performance in the presence of elastoplastic behaviour. Particular emphasis is placed on (i) mitigating effective stress oscillations and (ii) solving several two-phase, coupled, large deformation geotechnical problems. The numerical results confirm the suitability of the implicit B¯ GIMP-patch method for the solution of geotechnical problems spanning weak to strong hydro-mechanical coupling and small to large deformations.

Experimental and numerical investigation of the behavior of three-dimensional orthogonal woven composite plates under high-velocity impact

The performance of the three-dimensional orthogonal woven composites (3DOWC) under high-velocity impact is studied in a combined experimental and numerical way. The experimental impact velocity ranges from 155 to 1499 m/s. The impact processes are also simulated with mesoscopic point model and the material point method (MPM). The experimental and numerical results agree well in both the residual velocity and the configuration. Four failure patterns are observed for the perforated specimens. An empirical formula is constructed based on the experimental and numerical results.

Characterization of the Kinematic Evolution of the Hongshiyan Landslide Using the Material Point Method

In 2014, a landslide disaster occurred at Hongshiyan in Ludian County, Yunnan Province, China, causing the landslide-dames in Niulanjiang River. Scholars have studied the characteristics and causal mechanisms of this landslide and obtained substantial results. However, the kinematic evolution characteristics of the landslide remain relatively unclear. To resolve this problem, we introduced the Material Point Method (MPM) to study large-scale deformations for simulation analysis. The results showed that the movement of the slide body could be divided into three stages: accelerated sliding, decelerated sliding, and stabilizing. The velocity field and displacment field of the slide body is closely related to its spatial distribution. The velocity and displacement of the surface part higher than that of the shallow part. The internal friction angle and friction coefficient significantly affected the kinematic characteristics of landslide. The decrease in the internal friction angle and friction coefficient reduced the energy consumed by the friction between particles and between the particles and the sliding bed, raising the landslide velocity and displacement.

MPM modelling of debris flow entrainment and interaction with an upstream flexible barrier

Flexible barriers may be installed upstream in debris flow channels to reduce entrainment of bed material. Simulating both the entrainment and the impact on a barrier by the same numerical tool remains challenging. For this purpose, a three-dimensional one-phase material point method (MPM) software is used herein to back-calculate two large-scale flume experiments. These experiments were conducted to measure the entrainment of an erodible bed and the impact on a flexible barrier. To simulate the entrainment of the wet bed, a Mohr–Coulomb softening model is introduced. In the model, the apparent friction angle of the bed material decreases as a function of the distortional strain, effectively reproducing the pore pressure increase observed in the experiments. From the tests and the numerical simulations, we identify two main mechanisms leading to entrainment: (i) the direct rubbing and colliding effect of the flow on to the bed and (ii) a significant bed shear strength reduction. Concerning the first mechanism, existing models only consider the rubbing of the bed surface by a shear stress parallel to the slope. However, we observe that a ploughing-type erosion occurs due to normal stresses acting on the bed in the flow direction. The additional ploughing explains why beds which are mechanically stronger than the flow can also be partly entrained. Larger entrainment volumes are found when the bed material loses shear strength due to pore pressure buildup that eventually leads to a self-propelled entrainment where the bed no longer has frictional strength to carry its own weight.