Generalized Interpolation Material Point Method Research Articles

Multiphysics simulation of freezing and thawing granular media using material point method

In this paper, a fully coupled thermo-hydro-mechanical material point method, applicable to liquid-saturated porous systems undergoing large deformations and phase transitions, is presented. A mathematical framework was established based on multiphasic mixture theory and fundamental physical conservation laws, rather than using phenomenological or semi-empirical equations. A fractional-step-based semi-implicit solution scheme was proposed to solve the coupled formulations within the framework of the generalized interpolation material point method. The proposed method was validated using several benchmark examples, including the talik closure and thaw consolidation. Its performance in simulating climate-driven large deformation problems was further demonstrated by simulating the settlement of a rigid footing on thawing ground. This paper presents an innovative and rigorous framework for predicting the impact of climate change on engineering practices.

Study on copper-stainless steel explosive welding for nuclear fusion by generalized interpolated material point method and experiments

The thick copper stainless steel composite plate is an important component of the cooling coil terminal box of international nuclear fusion reactors. The composite rate, tensile strength, shear strength, and interface waveform of the metal plate are also far higher than the requirements of conventional explosive welding technology. It is difficult to obtain the best technical process parameters in a short time solely relying on conventional explosive welding tests. In order to solve the above-mentioned technical difficulties in explosive welding, this article applies the generalized interpolation material point method (GIMP) based on the explosive welding window, metal elastic-plastic mechanics, and explosive detonation theory to conduct macroscopic three-dimensional and microscopic two-dimensional numerical simulations of the copper stainless steel explosive welding process and the composite interface wave formation process, respectively. The experimental results demonstrate that the GIMP has significant advantages in numerical calculation and analysis for the explosive welding problem of high-speed impact collision of metal plates driven by explosive detonation, and it can effectively solve the technical problems of high technical specifications, low explosive processing composite rate, and low interface strength of large thickness copper stainless steel composite plates used in nuclear fusion.

Simulations of single and double shock experiments using generalized interpolation material point method with a noise control strategy

Simulations of single and double shock experiments using generalized interpolation material point method with a noise control strategy

Granular Material Point Method: unsaturated soil modelling

The paper proposed an enhancement to the Granular Material Point Method extending the original framework for unsaturated granular materials. It discusses briefly the key processes occurring during unsaturated flows and gives a set of assumptions for simplified analysis of such flows with the Granular Material Point Method. Then it proposes an algorithm for the Granular Material Point Method for unsaturated materials and shows how to adjust the original Granular Material Point Method code. Finally, the paper presents two sets of simulations involving unsaturated flows comparing outcomes from the previously proposed Granular Generalized Interpolation Material Point Method (Granular GIMP), original GIMP, as well as two newly proposed Granular GIMP simulations with an enhancement for unsaturated soils. The results show that the proposed formulation leads to improved and qualitatively different results and confirm that considering partial saturation is essential, also when the flow of material is of interest.The paper uniquely illustrates the developments not only with figures but also with videos, giving the whole extent of simulation instead of just a timestamped image.

Modeling of soil–rock mixture landslides with the generalized interpolation material point method

The new numerical model for studying the dynamic evolution of soil–rock mixture landslides is presented in this article. The numerical model based on the generalized interpolation material point method analyzes a simplified slope. The gravity is linearly loaded, and the linear elastic model is used to update the stress to obtain the initial state of the slope. A small soil cohesion is set to trigger the slope sliding until the equilibrium state is reached again. During this period, the elastic–plastic material model based on the Drucker–Prager criterion is adopted for soil and stones. The differences in dynamic evolution between the homogeneous soil slope and soil–rock mixture slope are studied. Under the same stone content, the influence of the size and shape of stone on the dynamic evolution of slope is studied.

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.

Effects of spatial autocorrelation structure for friction angle on the runout distance in heterogeneous sand collapse

This paper proposes a stochastic method for analyzing the runout distance of sand collapse considering the spatial variability of shear strength, in which random field theory and generalized interpolation material point method are integrated into a Monte-Carlo simulation basis. The random field is generated by Cholesky matrix decomposition method and implemented into the material point level, hence heterogeneity and large deformations are simultaneously considered in the modeling process. A sand collapse case is simulated with both homogeneous and heterogeneous condition assumptions by the proposed method. The effect of five theoretical autocorrelation functions (ACFs) on the runout distance of the collapse is highlighted since the ACFs are commonly adopted to characterize the spatial variability of soil properties due to sparse site observation data. It is shown that the deterministic analysis may underestimate the runout distance, while the heterogeneous model provides realistic results. Moreover, five ACFs and different coefficients of variation of friction angle (COVφ) are compared to investigate their influences on the runout distance modeling. The results show that the uncertainty of runout distance increases with the increase in COVφ. Meanwhile, the variances of the runout distance also become larger with COVφ increasing. Based on the proportion of the runout distance which exceeds the deterministic value, the results indicate that the deterministic analysis notably underestimates the risk induced by large runout distances in real heterogeneous granular flows (e.g., landslide, debris-avalanches).

An explicit GPU-based material point method solver for elastoplastic problems (ep2-3De v1.0)

Abstract. We propose an explicit GPU-based solver within the material point method (MPM) framework using graphics processing units (GPUs) to resolve elastoplastic problems under two- and three-dimensional configurations (i.e. granular collapses and slumping mechanics). Modern GPU architectures, including Ampere, Turing and Volta, provide a computational framework that is well suited to the locality of the material point method in view of high-performance computing. For intense and non-local computational aspects (i.e. the back-and-forth mapping between the nodes of the background mesh and the material points), we use straightforward atomic operations (the scattering paradigm). We select the generalized interpolation material point method (GIMPM) to resolve the cell-crossing error, which typically arises in the original MPM, because of the C0 continuity of the linear basis function. We validate our GPU-based in-house solver by comparing numerical results for granular collapses with the available experimental data sets. Good agreement is found between the numerical results and experimental results for the free surface and failure surface. We further evaluate the performance of our GPU-based implementation for the three-dimensional elastoplastic slumping mechanics problem. We report (i) a maximum 200-fold performance gain between a CPU- and a single-GPU-based implementation, provided that (ii) the hardware limit (i.e. the peak memory bandwidth) of the device is reached. Furthermore, our multi-GPU implementation can resolve models with nearly a billion material points. We finally showcase an application to slumping mechanics and demonstrate the importance of a three-dimensional configuration coupled with heterogeneous properties to resolve complex material behaviour.

Analysis of large deformation geotechnical problems using implicit generalized interpolation material point method

Analysis of large deformation geotechnical problems using implicit generalized interpolation material point method

A generalized interpolation material point method for modelling coupled thermo-hydro-mechanical problems

This paper proposes a Generalized Interpolation Material Point Method (GIMP) for modelling coupled thermo-hydro-mechanical (THM) processes within unsaturated porous media. The governing equations for the coupled thermo-hydro-mechanical problems are derived based on the conservation laws of mass, momentum and energy, and are discretized within the framework of the explicit three-phase single-point GIMP. The proposed THM-coupled GIMP is validated against available analytical solutions and FEM-based numerical solutions, and is used for simulating a climate-driven slope failure process involving both temperature variation and rainfall infiltration. The proposed THM-coupled GIMP is proved to be capable to capture the fully coupled thermo-hydro-mechanical process within unsaturated porous media associated with large deformations.

A Generalized Interpolation Material Point Method for Shallow Ice Shelves. 1: Shallow Shelf Approximation and Ice Thickness Evolution.

We develop a generalized interpolation material point method (GIMPM) for the shallow shelf approximation (SSA) of ice flow. The GIMPM, which can be viewed as a particle version of the finite element method, is used here to solve the shallow shelf approximations of the momentum balance and ice thickness evolution equations. We introduce novel numerical schemes for particle splitting and integration at domain boundaries to accurately simulate the spreading of an ice shelf. The advantages of the proposed GIMPM‐SSA framework include efficient advection of history or internal state variables without diffusion errors, automated tracking of the ice front and grounding line at sub‐element scales, and a weak formulation based on well‐established conventions of the finite element method with minimal additional computational cost. We demonstrate the numerical accuracy and stability of the GIMPM using 1‐D and 2‐D benchmark examples. We also compare the accuracy of the GIMPM with the standard material point method (sMPM) and a reweighted form of the sMPM. We find that the grid‐crossing error is very severe for SSA simulations with the sMPM, whereas the GIMPM successfully mitigates this error. While the grid‐crossing error can be reasonably reduced in the sMPM by implementing a simple material point reweighting scheme, this approach it not as accurate as the GIMPM. Thus, we illustrate that the GIMPM‐SSA framework is viable for the simulation of ice sheet‐shelf evolution and enables boundary tracking and error‐free advection of history or state variables, such as ice thickness or damage.

A Generalized Interpolation Material Point Method for Shallow Ice Shelves. 2: Anisotropic Nonlocal Damage Mechanics and Rift Propagation.

Ice shelf fracture is responsible for roughly half of Antarctic ice mass loss in the form of calving and can weaken buttressing of upstream ice flow. Large uncertainties associated with the ice sheet response to climate variations are due to a poor understanding of these fracture processes and how to model them. Here, we address these problems by implementing an anisotropic, nonlocal integral formulation of creep damage within a large‐scale shallow‐shelf ice flow model. This model can be used to study the full evolution of fracture from initiation of crevassing to rifting that eventually causes tabular calving. While previous ice shelf fracture models have largely relied on simple expressions to estimate crevasse depths, our model parameterizes fracture as a progressive damage evolution process in three‐dimensions (3‐D). We also implement an efficient numerical framework based on the material point method, which avoids advection errors. Using an idealized marine ice sheet, we test the creep damage model and a crevasse‐depth based damage model, including a modified version of the latter that accounts for damage evolution due to necking and mass balance. We demonstrate that the creep damage model is best suited for capturing weakening and rifting over shorter (monthly/yearly) timescales, and that anisotropic damage reproduces typically observed fracture patterns better than isotropic damage. Because necking and mass balance can significantly influence damage on longer (decadal) timescales, we discuss the potential for a combined approach between models to best represent mechanical weakening and tabular calving within long‐term simulations.

Simulating penetration problems in incompressible materials using the material point method

This paper presents a methodology for computing the response of a rigid strip footing in incompressible Tresca soil when loaded to large settlements. The numerical simulations were performed using the generalized interpolation material point method (GIMP). For efficiency, a block-structured rectilinear irregular grid was used that moves and compresses as the footing advances. Volumetric locking was prevented using the non-linear extension to the B-bar method. The paper addresses the modifications required for the implementation of the B-bar method in GIMP and demonstrates its efficacy in mitigating locking using two benchmark problems: the Cook’s membrane problem and the limit bearing capacity of a footing in a Tresca soil at small settlements. The response of the footing when loaded to large settlements under both quasi-static and dynamic loads is then presented. A comparison of the solutions obtained using the proposed methodology with other numerical solutions available in the literature illustrates the efficacy of the proposed method.

Postfailure Analysis of Slopes by Random Generalized Interpolation Material Point Method

Abstract In this paper, the generalized interpolation material point (GIMP) method will be utilized to simulate the postfailure behavior of slopes that accounts for spatial variability. Because the...

Analysis of the run-out processes of the Xinlu Village landslide using the generalized interpolation material point method

The prediction of the landslide kinetic features is of great importance in minimizing the potential hazardous impacts and in applying the appropriate stabilization techniques. The present study used the generalized interpolation material point (GIMP) method to analyze the run-out processes of the Xinlu Village landslide that has taken place in Xinlu Village, Chongqing, China, in 2016. The evolutions of equivalent plastic strain, displacement, landslide velocity, and kinematic energy were investigated during the landslide motion. The simulation results indicated that the initial stage of the landslide started with slippage of the mid-front soil part with a maximum velocity of 1.02 m/s (at t = 9 s). The rear rock came to failure at t = 69 s as the tensile crack extended from the landslide surface to the deep weak interlayer. Thereafter, the rear rock further accelerated and pushed the mid-front sliding soil, which formed an overall movement. The kinetic energy of the studied landslide concentrated in the acceleration phases of the soil and rock masses. The predicted landslide geometry and run-out distance had slight differences from the actual ones. Based on the landslide run-out analysis, the studied landslide can be classified as a landslide that simultaneously comprises retrogressive and advancing features. A potential secondary failure of this landslide could happen under specific extreme circumstances.

Stabilized generalized interpolation material point method for coupled hydro-mechanical problems

The material point method (MPM) has been increasingly used to simulate coupled hydro-mechanical problems involving large deformations. However, when addressing saturated porous media with an almost incompressible liquid phase, the classic explicit MPM with low-order interpolation functions is not stable if no further stabilization approach is used. In this study, a solid-velocity–liquid-velocity-based hydro-mechanical governing formulation is adopted to construct a two-phase single-point explicit generalized interpolation material point (GIMP) method. To stabilize this set of formulation, the XPIC(m) (extended PIC of order m) method is extended to erase null space noise and damp high-frequency waves in both solid and liquid phases; additionally, a cell-based averaging approach is adopted to solve locking issues and smooth stress field variables. Several numerical examples have been presented to demonstrate the capabilities of the stabilized coupled GIMP method in simulating coupled hydro-mechanical problems involving dynamic effects and large deformations.

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

In this paper, a computational framework based on the material point method (MPM) is developed to study the coupled seepage-erosion-deformation process within unsaturated soils. Based on the mixture theory, the unsaturated erodible soil is conceptualized as a three-phase multi-species porous medium, which is represented as a set of Lagrangian material points in a three-phase multi-species single point MPM framework. Governing equations as well as constitutive models for describing the coupled seepage-erosion-deformation behaviour within unsaturated erodible soils are presented: the solid skeleton is modelled as an elasto-plastic material; the pore water is treated as a weakly compressible fluid; while the fine particles in the solid matrix can be eroded and transferred into liquidised fine particles, and transported with the flowing liquid. This governing system is discretised with the generalized interpolation material point (GIMP) method and solved explicitly. The proposed coupled seepage-erosion-deformation GIMP is validated via three numerical examples and then employed for simulating the rainfall-induced slope failure process involving internal erosion. Thanks to the capability of the MPM in capturing large deformations, the evolution of the coupled seepage-erosion-deformation behaviour during the whole slope failure process can be obtained. This suggests that the proposed coupled GIMP framework is a promising approach for future studies of internal erosion problems in unsaturated soils involving complex multi-couplings of seepage flow, phase change and large deformations, which are difficult to be modelled by traditional mesh-based methods.

Combining peridynamics and generalized interpolation material point method via volume modification for simulating transient responses

By using nonlocal discrete force functions, peridynamics (PD) can effectively deal with the problems involving discontinuities and singularities. As a continuum-based particle method, the material point method (MPM) and its advanced version, generalized interpolation material point method (GIMP), use local and nonlocal spatial discretization, respectively, to effectively simulate large deformations and multi-phase (solid–fluid–gas) interactions via mapping and remapping between material points and associated background nodes. However, nonlocal constitutive modeling has rarely been employed in the MPM or GIMP for simulating failure evolution. To combine the strengths of both PD and MPM/GIMP for better simulating the failure evolution under transient loading, an attempt is made to eliminate the limitation in the original PD due to the volume integration so that both MPM/GIMP and PD could be smoothly combined via volume modification. One-dimensional examples are employed to demonstrate and verify the proposed volume modification peridynamics and its combination with MPM/GIMP.

Numerical simulation of granular mixing in a rotary drum using a generalized interpolation material point method

AbstractNumerical simulations using a generalized interpolation material point method (GIMP) and material point method were introduced into the studying of granular mixing in a rotary drum. A Drucker–Prager model that has an equal size with a Mohr–Coulomb criterion was adopted to predict the failure behavior of granular matter. Experiments and discrete element method simulations were conducted to validate the models, and GIMP was finally used due to its accuracy and the ability for eliminating the crossing boundary noise. Velocity field of bed surface and standard deviation were used to measure the mixing performance. In particular, the influence of mesh size, elastic modulus, cohesion, and filling level were investigated. The results of simulations show that the utilization of GIMP significantly reduces the computing cost of simulation. The analysis of mixing performance shows that mixing performance decreases with the increase of elastic moduli, cohesion of granular matter, and filling levels.

Application of the Generalized Interpolation Material Point Method Coupled With the Finite Element Method for Rigid-Flexible Contact

The paper shows the numerical simulation of the Generalized Interpolation Material Point Method (GIMP) coupled with the Finite Element Method (FEM) in rigid-flexible contact. The GIMP can overcome certain numerical noise existing in the original MPM and is used to simulate the great deformation of soft materials. A rigid material with a higher hardness can be described by the finite element method for limited deformation in rigid-flexible contact. First, the feasibility of GIMP was verified by the high-speed gelatin impact rigid wall. After that, this article shows the collision simulation of an iron bar and a gelatin bar. By comparing the material deformation, internal pressure distribution and the form of shock-wave obtained by GIMP with the calculation results of ls-dyna, it is shown that couple the GIMP and finite element method to deal with rigid-flexible contact is feasible.