Material Point Method Research Articles

Failure of levees induced by toe uplift: Investigation of post-failure behavior using material point method

Levees are essential structures in flood defense systems, and their failures can lead to devastating consequences on the surrounding territories. One of the failure mechanisms mostly controlled by the foundation soil stratigraphy is the instability of the land side slope, triggered by the development of high uplift pressures in the foundation. This complex phenomenon has been investigated experimentally with centrifuge tests or large-scale tests and numerically with the limit equilibrium method (LEM) and the finite element method (FEM). In this work, we applied a multiphase formulation of the material point method (MPM) to analyze the development of toe uplift instability mechanism, from the onset of failure to large displacements. The numerical model is inspired by an experiment carried out in a geotechnical centrifuge test by Allersma and Rohe (2003). The comparison with the experiment allows for understanding critical pore pressure triggering large displacements in the foundation soils. Moreover, we numerically evaluated the impact of different values of foundation soils' hydraulic conductivity on the failure mechanism. The results show that hydraulic conductivity mainly influences the time of failure onset and the extension of shear localization at depth. Finally, the advantages of using large displacement approaches in the safety assessment of earth structures are discussed. Unlike FEM, there are no issues with element distortions generating difficulties with numerical convergence, allowing for full post-failure reproduction. This capability permits precise quantification of earth structure damages and post-failure displacements. The ensuing reinforcement systems' design is no longer over-conservative, with a significant reduction in associated costs. ©2022 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Simulation of Bayonet Chamber Process Based on CFEMP

The bayonet chamber process is accompanied by severe transient elastic-plastic deformation. Meanwhile, the shape of the rotating band is complex. The Finite Element Method (FEM) suffers from mesh distortion when numerical calculating such cases. In this paper, the projectile and rotating band are discretized by material points while the barrel is discretized by finite elements. The node-surface contact algorithm is applied to describe the interaction of the parts. The Coupled Finite Element Material Point Method (CFEMP) model of the projectile band bayonet-chamber process is established. The resistance acting on the rotating band and the velocity of the projectile are obtained. The results can provide a reference for the projectile conveying design and the determination of bayonet-chamber velocity.

A conservation law consistent updated Lagrangian material point method for dynamic analysis

The Material Point Method (MPM) is well suited to modelling dynamic solid mechanics problems undergoing large deformations with non-linear, history dependent material behaviour. However, the vast majority of existing material point method implementations do not inherit conservation properties (momenta and energy) from their continuum formulations. This paper provides, for the first time, a dynamic updated Lagrangian material point method for elasto-plastic materials undergoing large deformation that guarantees momenta and energy conservation. Sources of energy dissipation during point-to-grid and grid-to-point mappings for FLuid Implicit Particle (FLIP) and Particle In Cell (PIC) approaches are clarified and a novel time-stepping approach is proposed based on an efficient approximation of the Courant-Friedrich-Lewy (CFL) condition. The formulation provided in this paper offers a platform for understanding the energy conservation nature of future/existing features of material point methods, such as contact approaches.

Two-Phase MPM Simulation of Surge Waves Generated by a Granular Landslide on an Erodible Slope

A high-speed debris flow sliding into a reservoir can cause a huge disaster. Consequently, predicting landslide movement accurately and its potential interaction with water is crucial. This paper developed a computational model based on a two–layer two–phase material point method (MPM) to simulate surge waves generated by granular landslides on an erodible slope. By comparing granular landslide on a rigid and erodible slope, the effect of the slope erodibility on the process of landslide movement and the waves generated is investigated. The model takes full account of the large deformations, fluidisation and settlement of granular material in soil–water interactions. The numerical model is validated by comparing the simulated results with experimental data. The influences of internal friction angle, density, elastic modulus, Poisson ratio and dilatancy angle on wave height are also studied. The validated model was then used to investigate the surge waves generated by dry and saturated granules sliding along a rigid and erodible slope. The results show that both the erodible slope and saturated granular slide can increase the first wave crest height generated by the landslide.

Physical and Numerical Simulation of the Mechanism Underpinning Accumulation Layer Deformation, Instability, and Movement Caused by Changing Reservoir Water Levels

Large-scale physical models of landslides can potentially accurately reflect the interactions between many internal and external factors and elucidate the process of slope deformation and failure. In order to reveal the mechanism of deformation of the reservoir bank accumulation layer, in this study, a large-scale physical test model with a similarity ratio of 1:200 was constructed based on the actual engineering geological section. Two reservoir water level cycle fluctuation conditions were simulated, and the reservoir water level drop rate was strictly controlled to be two times the rise rate. This study analyzed pore water pressure and deformation characteristics in the accumulation layer in relation to fluctuating reservoir water levels. The results showed that the rise in reservoir water level will make landslides more stable. The periodic sudden drop in water level seriously endangers the stability of landslides. The deformation and failure of landslides are more likely to occur in the weak interlayer area. The failure mode of the accumulation body in the test was traction failure. It is suggested that the front part of the accumulation body can be reinforced in practical engineering. To reveal the progression of instability and movement during accumulation layer large-scale landslides, a numerical model was constructed using the material point method. The accumulation layer sliding process could be divided into three stages: acceleration sliding, deceleration sliding and stabilization. After destabilization, the river channel may be altered by the landslide mass to form a landslide dam, potentially threatening the integrity of the dam via impulse waves generated during destabilization. The research results provide technical support for reservoir scheduling in major water conservancy and hydroelectric power station reservoirs as well as engineering risk assessment and prevention.

Modelling large-scale landslide using a GPU-accelerated 3D MPM with an efficient terrain contact algorithm

The material point method (MPM) simulation of large-scale landslides can provide useful information to response to landslide hazards in mountainous regions. However, the structured background meshes commonly adopted in MPM fail to accurately capture the complex terrain above which the sliding mass moves. In this work, a novel terrain contact algorithm is proposed and integrated into a GPU-accelerated 3D MPM to model large-scale landslides. The complex terrain is modelled by a fixed triangular surface mesh generated according to the digital elevation model (DEM) and the interaction between the sliding mass and the basal surface is modelled by a contact algorithm between the triangular surface mesh and the material points. Furthermore, a contact detection algorithm based on level-set functions is developed to improve the contact detection efficiency. The detailed computational formulations and numerical implementation based on GPU parallel computing are presented. After the correctness and the efficiency being verified by two numerical examples, the proposed method is applied to simulate the catastrophic Baige landslide that occurred in China in 2018. The results indicate that the present method is both accurate and efficient and can provide a useful tool for numerical study on landslides.

Addressing complexities in MPM modeling of calibration chamber cone penetrometer tests in homogenous and highly interlayered soils

Cone penetrometer tests (CPTs) are used to characterize soil for a variety of geotechnical engineering applications, including earthquake-induced liquefaction triggering assessment. Numerical modeling of CPTs is frequently used to better understand soil behavior, soil-penetrometer interaction, and engineering estimates made from CPT data. However, calibrating and validating numerical CPT simulations with experimental calibration chamber (CC) data can be challenging. Specifically, uncertainties in the interpretation of laboratory strength and compression data compound with uncertainties in the CC testing and the assumptions made when developing the numerical model. This article provides a comprehensive review of uncertainties in the calibration and validation of CPT numerical simulations performed in homogenous sand, homogenous clay, and layered sand-clay soil profiles, comparing numerical results with well-documented experimental calibration chamber tests performed at Deltares. In particular, the Material Point Method (MPM) is used to perform the numerical analyses. A framework is presented to assess how uncertainty in the numerical model output is attributed to each input parameter. It is demonstrated that uncertainties can be explored numerically. Finally, recommendations for future experimental and numerical studies of CPTs are provided.

Two-phase MPM modelling of debris flow impact against dual rigid barriers

Multiple barriers are usually installed to effectively mitigate large-volume debris flows. Existing multiple-barrier design recommendations ignore the effects of solid–fluid interaction and may cause uncertainties in estimating the flow impact force on subsequent barriers. In this study, a fully coupled, two-layer, two-phase material point method with an incompressible fluid phase is implemented and validated using the experimental results of dry sand, water and sand–water mixture flows impacting on rigid barriers. Numerical parametric study is carried out using the validated model to investigate the effects of Froude number (Fr) and barrier spacing on second barrier impact force. A debris flow volume of 500 m3 is modelled, with the Fr ranging from 2 to 6; these are values relevant to the gentle and steep terrains in Hong Kong. Simulation results show the importance of changes in fluidisation ratio, which is the ratio of basal pore fluid pressure and total stress. The debris flow, after impacting the first barrier, overflows and lands on the slope between the two barriers. The fluidisation ratio of debris flow after landing increases by up to 30%, leading to an increase of impact velocity at the second barrier by up to 80%. Consequently, the impact force of debris flows on the second barrier is underestimated by up to 50% compared with existing design guidelines. This implies that neglecting the fluidisation ratio may lead to non-conservative design of multiple barriers.

Microstructural controls on the plastic consolidation of porous brittle solids

Through stochastic-numerical microstructure-based experiments, the plastic consolidation under compression of porous brittle solids, with porosities from 0.25 to 0.75 and a large variety of microstructural characteristics, has been investigated. This was made possible by generating microstructures from Gaussian random fields in order to obtain stochastic ensembles of structures with prescribed properties, which are then simulated within the material point method. Below a critical imposed strain rate, the consolidation behavior is found to be very weakly affected by the degree of heterogeneity and anisotropy. Structures where the solid phase takes up more space than the void phase have a consolidation response approximately independent of the structural geometry and dimensionality (comparing two- and three-dimensional structures). Finally, we show that the consolidation of two-dimensional structures collapses on a single master curve that can be described by a simple function similar to one presented for a completely different system, namely a system of interacting discrete cohesive disks. In this function, we report a universal parameter largely independent of material specifications.

Elastoplastic Damage Modeling of Rock Spalling/Failure Induced by a Filled Flaw Using the Material Point Method (MPM)

Elastoplastic Damage Modeling of Rock Spalling/Failure Induced by a Filled Flaw Using the Material Point Method (MPM)

Modeling footing resting on anisotropic sand using material point method

Sand typically exhibits anisotropic internal structure which may significantly influence its mechanical behavior. The material point method (MPM) can eliminate mesh distortion and thus is suitable for investigating geotechnical problems with large deformation. In this study, an advanced anisotropic critical state theory (ACST)-based soil model is implemented in MPM to study the response of strip footing resting on anisotropic sand. The capability of the model is verified by simulating several element tests and strip footing tests with different soil densities and fabric bedding plane orientations. For the footing problem with a vertical load, as the fabric bedding plane orientation increases, the bearing capacity decreases and its corresponding settlement increases. The failure pattern becomes asymmetrical when the bedding plane orientation or the loading direction is inclined. A comparison between the simulation results predicted by the anisotropic and isotropic models is made, which demonstrates that neglecting the fabric anisotropy may lead to the overestimation of the bearing capacity.

Fundamental abrasive contact at high speeds: Scratch testing in experiment and simulation

The understanding and experimentation of abrasive wear mechanisms at high speeds is still poorly investigated in literature. This is mainly due to a lack of suitable, well-instrumented test rigs for fundamental, single abrasive wear events. Standard scratch tests, which are often utilized for studies of abrasion phenomena, operate in the low-speed range up to some mm/s, while applications suffering from abrasive wear often operate at speeds exceeding 1 m/s (e.g., rolling, grinding, machining).Numerical approaches, especially particle-based methods, allow the simulation of such fast deformation processes, but rely on hardening models that require a precise knowledge of material parameters. Thus, the Johnson-Cook material model was parametrized using data from high-speed compression tests of pure aluminum. A series of scratch tests with increasing depths were then simulated using the particle-based Material Point Method (MPM). Experimentation was done on a pendulum scratch test rig equipped with a Rockwell C diamond cone. By adjusting the balance point of the swing arm of ∼1 m length, a velocity of 6.8 m/s was achieved at its tip as measured with a high-speed camera. Scratches of several depths were performed, and their force signals acquired. Post-test analyses comprised topography measurements and EBSD on cross-sections of the scratches to investigate the microstructural changes due to the high-speed wear event.Scratch topographies and abrasive mechanisms compared favorably between experiment and simulation for the aluminum. The extent of strain hardening was significantly reduced compared to low-speed experiments. The calibration of the high-speed force sensor was successful and now allows the investigation of new alloys and determination of material parameters under high-speed abrasive conditions.

An explicit phase field material point method for modeling dynamic fracture problems

AbstractA novel explicit phase field material point method (ex‐PFMPM) is proposed for modeling dynamic fracture problems. The rate‐dependent phase field governing equation is discretized by a set of particles, and the phase field is updated by the explicit forward‐difference time integration. Furthermore, the stability of the ex‐PFMPM is studied. A novel explicit critical time step formula is obtained based on the system eigenvalues in one dimension and then extended to two and three dimensions. The critical time step formula takes the effect of particle position and neighboring cell interaction into consideration, and can also be used in an explicit phase field finite element method. Several numerical examples, including a dynamic crack branching, a plate with pre‐existing crack under velocity boundary conditions and a three point bending problem are studied to verify the proposed ex‐PFMPM. The use of the history field in the explicit method is studied, which shows that it will lead to fake phase field update and overestimation of the fracture energy in the unloading case. All of the numerical results show that the proposed ex‐PFMPM has the capacity of modeling the crack initiation and propagation problems with both accuracy and efficiency.

Modeling strip footings on slopes using the material point method

Modeling strip footings on slopes using the material point method

Coseismic site response and slope instability using periodic boundary conditions in the material point method

This paper proposed the explicit generalized-α time scheme and periodic boundary conditions in the material point method (MPM) for the simulation of coseismic site response. The proposed boundary condition uses an intuitive particle-relocation algorithm ensuring material points always remain within the computational mesh. The explicit generalized-α time scheme was implemented in MPM to enable the damping of spurious high frequency oscillations. Firstly, the MPM was verified against finite element method (FEM). Secondly, ability of the MPM in capturing the analytical transfer function was investigated. Thirdly, a symmetric embankment was adopted to investigate the effects of ground motion arias intensity (Ia), geometry dimensions, and constitutive models. The results show that the larger the model size, the higher the crest runout and settlement for the same ground motion. When using a Mohr-Coulomb model, the crest runout increases with increasing Ia. However, if the strain-softening law is activated, the results are less influenced by the ground motion. Finally, the MPM results were compared with the Newmark sliding block solution. The simplified analysis herein highlights the capabilities of MPM to capture the full deformation process for earthquake engineering applications, the importance of geometry characterization, and the selection of appropriate constitutive models when simulating coseismic site response and subsequent large deformations.

Mechanics–thermotics–chemistry coupling response model and numerical simulation method for reactive liner

Aiming at describing the mechanics–thermotics–chemistry coupling response of the reactive material liner under impact loading, the Grüneisen equation of state in the form of P–V–T was derived. Combined with the impact temperature rise theory, heat conduction theory, and Arrhenius chemical reaction kinetic model, the mechanics–thermotics–chemistry coupling response model is established. A numerical simulation framework for the thermodynamic response of reactive materials under impact load was established, and numerical simulation codes for the impact-induced energy release behavior of reactive materials was developed based on the material point method, which realized the numerical simulation of the formation behavior of the reactive material penetrator (jet) under explosion load. The results show that chemical reactions occur in the process of reactive material jet formation, and high temperature and high pressure products make the jet expand and thicken constantly, resulting in the decrease in the density of the jet head and the increase in the cross-sectional area. As such, the jet has hardly any armor-piercing capability at stand-offs of 2.5 times the caliber, and the simulation results are in good agreement with the experimental results.

Post-failure analysis of landslide blocking river using the two-phase double-point material point method: a case of western Hubei, China

Post-failure analysis of landslide blocking river using the two-phase double-point material point method: a case of western Hubei, China

Analysis and mitigation of spatial integration errors for the material point method

SummaryThe material point method (MPM) is a robust numerical simulation approach for continuum mechanics problems involving large material deformations coupled to changing surface topographies. These types of problems are present in many different engineering contexts, from understanding the failure processes of earthen slopes to predicting the strengths and failure mechanisms of body armor to modeling the impact forces of waves in fluid tanks. By using a set of persistent material point tracers to follow the motion and deformation of the continuum material while solving the equations of motion on a static simulation grid, the MPM avoids several shortcomings of more traditional numerical approaches including blurring of material surfaces — as in Eulerian finite element or finite volume methods (FEMs or FVMs) — and mesh tangling — as in Lagrangian FEMs. Despite its robustness, MPM is known to develop significant numerical errors: namely, (i) the particle ringing instability and (ii) solution dependent discretization and integration errors. In this work, we present an analysis of local‐in‐time, spatial integration errors in the MPM and several techniques designed to mitigate these errors. Error mitigation approaches previously described in the literature are compared to a new method we propose for problems involving very large material deformations. The proposed method is shown to offer substantial improvement over standard MPM for simulations of fluid‐like materials without requiring significant augmentation of existing MPM frameworks.

Analysis of a landslide in sensitive clays using the material point method

Slope movements are generally classified into four different phases: pre-failure, failure, post-failure and eventual reactivation. In engineering applications, the pre-failure and failure phases are usually analysed using traditional numerical techniques, such as the finite-element method and the finite-difference method. However, these methods are often based on the assumption of small deformations and consequently are unsuitable for analysing the slope behaviour during the post-failure stage, which is usually characterised by very large deformations. To overcome this shortcoming, the material point method (MPM) is employed in the present study. Specifically, MPM is used to perform an analysis of a landslide in sensitive clays that occurred at Saint-Jude (Quebec, Canada) in 2010. To assess the accuracy of the analysis, the final profile and the displacement magnitude detected after the event are compared with those obtained by the numerical simulation. The results provided by MPM are in satisfactory agreement with field observations. The failure mechanism and the development of the failure surface within the slope are also reproduced successfully. These results also show that MPM is an attractive method for analysing the kinematics of landslides in sensitive clays, requiring also a limited number of conventional geotechnical parameters as input data.

Topology optimization of locomoting soft bodies using material point method

Topology optimization methods have widely been used in various industries, owing to their potential for providing promising design candidates for mechanical devices. However, their applications are usually limited to the objects which do not move significantly due to the difficulty in computationally efficient handling of the contact and interactions among multiple structures or with boundaries by conventionally used simulation techniques. In the present study, we propose a topology optimization method for moving objects incorporating the material point method, which is often used to simulate the motion of objects in the field of computer graphics. Several numerical experiments demonstrate the effectiveness and the utility of the proposed method.