Material Point Method Research Articles

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.

Extended B‐spline‐based implicit material point method enhanced by F‐bar projection method to suppress pressure oscillation

SummaryAn enhancement of the extended B‐spline‐based implicit material point method (EBS‐MPM) is developed to avoid pressure oscillation and volumetric locking. The EBS‐MPM is a stable implicit MPM that enables the imposition of arbitrary boundary conditions thanks to the higher‐order EBS basis functions and the help of Nitsche's method. In particular, by means of the higher‐order EBS basis functions, the EBS‐MPM can suppress the cell‐crossing errors caused by material points crossing the background grid boundaries and can avoid both the stress oscillations arising from inaccurate numerical integration and the ill‐conditioning of the resulting tangent matrices. Although the higher‐order EBS basis functions are known to avoid volumetric locking, the problem of pressure oscillation has not yet been resolved. Therefore, to suppress pressure oscillation due to quasi‐incompressibility, we propose the incorporation of the F‐bar projection method into the EBS‐MPM, which is compatible with the higher‐order EBS basis functions. Three representative numerical examples are presented to demonstrate the capability of the proposed method in suppressing both the pressure oscillation and volumetric locking. The results of the proposed method are compared to those of the finite element method with F‐bar elements and those of isogeometric analysis with quadratic NURBS elements.

An Improved Material Point Method with Aggregated and Smoothed Bernstein Functions

Nodal shape functions and their gradients are vital in transferring physical information within the material point method (MPM). Their continuity is related to numerical stability and accuracy, and their support domain size affects computational efficiency. In this paper, a scheme of aggregated and smoothed Bernstein functions is proposed to improve the MPM. In detail, the Bernstein polynomials are smoothed with a convolution reformation to eliminate the cell crossing error, and an aggregation strategy is implemented to cut down the node amount required for field probing. Hierarchical MPM variants are obtained with choices of original Bernstein polynomials and degrees of smoothing. Numerical examples show that mass, momentum, and energy conservations are all well met, and no cell crossing noise exists. In addition, solution accuracy and numerical stability are significantly improved in large deformation problems.

Towards a multi-abrasive grinding model for the material point method

An efficient optimization of surface finishing processes can save high amounts of energy and resources. Because of the large occurring deformations, grinding processes are notoriously difficult to model using standard (mesh-based) micro-scale modeling techniques. In this work, we use the meshless material point method to study the influence of abrasive shape, orientation, rake angle, and infeed depth on the grinding result. We discuss the chip morphology, the surface topography, cutting versus plowing mode, the material removal rate, and the chip temperature. A generalization of our model from a straightforward single-abrasive approach to a multiple-abrasive simulation with pseudo-periodical boundary conditions greatly increases the degree of realism and lays the foundation for comparison with real finishing processes. We finally compare our results for multiple abrasives to those obtained for a scaled-down molecular dynamics system and discuss similarities and differences.

Substratum virtualization in three-dimensional landslide modeling with the material point method

The material point method is a first-line choice in modeling large-deformation problems and has been widely utilized to investigate landslide dynamics. However, topographic complexity and computational demand have often hindered three-dimensional implementations. Here, we propose an algorithm for the virtualization of the substratum, in which the latter can be defined on a regular background grid as a non-zero kinematic boundary condition permitting frictional contact. In this setup, the computational power can be fully employed to model the moving mass. To evaluate the algorithm, we successfully simulated a rolling ball and flume experiments. Then, we took the Yanyuan landslide (27°29′25”N, 101°01′38″E) as an example to test the performance in a real case. By speeding up computation by ∼90 times, we argue that the proposed algorithm can promote accurate three-dimensional modeling of landslides and facilitate physically-based hazard assessments.

A concurrent multiscale method based on smoothed molecular dynamics for large-scale parallel computation at finite temperature

A concurrent atomic-to-continuum multiscale method for finite-temperature simulation with large-scale parallel computation is developed. Seamless and stable coupling between molecular dynamics (MD) method and continuum-based material point method (MPM) is achieved with the aid of mesoscopic smoothed molecular dynamics (SMD) method. Novel techniques are proposed to filter spurious high-frequency reflections and bridge different thermal descriptions in atomistic and continuum models by adopting the efficient Markovian generalized Langevin equation (GLE) with newly designed drift matrix. Besides, an effective relaxation strategy is developed to fully relax the multiscale model to thermodynamic equilibrium state. The concurrent multiscale method can be effectively parallelized within the parallel computation framework of particle-grid dual discretization, and its efficiency when executing on large-scale computation clusters is analyzed in detail. The contact-sliding and particle impact examples are calculated with the proposed method to demonstrate its superiority as an effective numerical tool in the practical applications.

Model reduction for the material point method via an implicit neural representation of the deformation map

This work proposes a model-reduction approach for the material point method on nonlinear manifolds. Our technique approximates the kinematics by approximating the deformation map using an implicit neural representation that restricts deformation trajectories to reside on a low-dimensional manifold. By explicitly approximating the deformation map, its spatiotemporal gradients—in particular the deformation gradient and the velocity—can be computed via analytical differentiation. In contrast to typical model-reduction techniques that construct a linear or nonlinear manifold to approximate the (finite number of) degrees of freedom characterizing a given spatial discretization, the use of an implicit neural representation enables the proposed method to approximate the continuous deformation map. This allows the kinematic approximation to remain agnostic to the discretization. Consequently, the technique supports dynamic discretizations—including resolution changes—during the course of the online reduced-order-model simulation.To generate dynamics for the generalized coordinates, we propose a family of projection techniques. At each time step, these techniques: (1) Calculate full-space kinematics at quadrature points, (2) Calculate the full-space dynamics for a subset of ‘sample’ material points, and (3) Calculate the reduced-space dynamics by projecting the updated full-space position and velocity onto the low-dimensional manifold and tangent space, respectively. We achieve significant computational speedup via hyper-reduction that ensures all three steps execute on only a small subset of the problem's spatial domain. Large-scale numerical examples with millions of material points illustrate the method's ability to gain an order of magnitude computational-cost saving—indeed real-time simulations—with negligible errors.