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MPM procedure: a particle-to-grid (P2G) transfer, b nodal update, c grid-to-particle (G2P) transfer, d particle update
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Granular impact—the dynamic intrusion of solid objects into granular media—is widespread across scientific and engineering applications including geotechnics. Existing approaches to the simulation of granular impact dynamics have relied on either a purely discrete method or a purely continuum method. Neither of these methods, however, is deemed opt...
Citations
... A coupled MPM and DEM model with a boundary contact algorithm was used to back-analyze experimental results and conduct a parametric study (Al-Kafaji 2013;Jiang et al. 2016;Jiang et al. 2022). The granular flow is governed by the mo-mentum equation ...
... The normal reaction component f n can be determined based on a normal stiffness constant k N , MP mass m p , and residual distance ξ , which is calculated in eq. 4 (i.e., Fig. 3a) (Jiang et al. 2022): ...
... At the end of the diversion wall, the foot of the perpendicular from the MP center falls outside of the line segment of the diversion wall (Fig. 3c). The contact algorithm is modified based on Jiang et al. (2022) to consider the residual distance when the foot of the perpendicular from the MP center is not within the wall line segment. The penetration distance is taken as the distance between the contact end and the MP center. ...
In sparsely populated and rural areas, government agencies propose the installation of V-shaped diversions to mitigate flow-type landslides. In contrast to rigid barriers, diversions are small, easy-to-construct, and cost-effective. Nonetheless, the impact dynamics of flow-type landslides against diversion structures remains unclear and hinders the development of scientific-based design guidelines. Diversion angles that are too large decelerates the flow and causes an overspill. In contrast, diversion angles that are too small results in long walls that are not feasible to construct. In this study, laboratory-scale flume experiments modeling the impact of dry sand against diversions are conducted. The experimental data are used to validate a coupled material point method and discrete element method numerical model. The numerical model is used to conduct a parametric study to investigate the effects of post-impact flow. The transition from attached oblique to detached bow shocks occurs with decreasing inflow and increasing diversion angle, causing the largest flow runup height at the diversion side rather than the diversion apex. It is proposed to design diversions based on bow and oblique shock mechanisms. Design charts that consider the competing effects between deflected and accumulated state are proposed. The newly proposed analytical model for predicting deflection height to mitigate overspill shows close agreement with experimental results.
... However, when the material undergoes large and nonuniform deformations, translations, or rotations, the mesh in FEM can become ill-shaped [9], affecting its computational accuracy. Therefore, some continuum methods suited for large deformations, such as the material point method (MPM), have also been used to model fine grains and coupled with DEM [13][14][15]. ...
A two-way coupling numerical framework based on smoothed particle hydrodynamics (SPH) is developed in this study to model binary granular mixtures consisting of coarse and fine grains. The framework employs updated Lagrangian SPH to simulate fine grains, with particle configurations updated at each time step, and total Lagrangian SPH to efficiently model coarse grains without updated particle configurations. A Riemann solver is utilized to introduce numerical dissipation in fine grains and facilitate their coupling with coarse grains. To enhance computational efficiency, a multiple time-stepping scheme is initially applied to manage the time integration coupling between coarse and fine grains. Several numerical experiments, including granular column collapse, low-speed impact craters, and granular flow impacting blocks, are conducted to validate the stability and accuracy of the
proposed algorithm. Subsequently, two more complex scenarios involving a soil-rock mixture slope considering irregular coarse particle shapes, and bouldery debris flows on natural terrain, are simulated to showcase the potential engineering applications. Finally, a detailed analysis is performed to evaluate the computational efficiency advantages of the present approach. The findings of this study are consistent with previous experimental and numerical results, and the implementation of a multiple time-stepping scheme can improve computational efficiency by up to 600%, thereby providing significant advantages for large-scale
engineering simulations.
... Based on the discrete element theory, a commercial discrete element software, particle fl ow code (PFC), was developed. The mesoscopic mechanical responses of soils have been studied using the abovementioned discrete element software, and several results have been obtained (Wu et al., 2020;Jiang et al., 2022). ...
Expanded polystyrene (EPS) particle-based lightweight soil, which is a type of lightweight filler, is mainly used in road engineering. The stability of subgrades under dynamic loading is attracting increased research attention. The traditional method for studying the dynamic strength characteristics of soils is dynamic triaxial testing, and the discrete element simulation of lightweight soils under cyclic load has rarely been considered. To study the meso-mechanisms of the dynamic failure processes of EPS particle lightweight soils, a discrete element numerical model is established using the particle flow code (PFC) software. The contact force, displacement field, and velocity field of lightweight soil under different cumulative compressive strains are studied. The results show that the hysteresis curves of lightweight soil present characteristics of strain accumulation, which reflect the cyclic effects of the dynamic load. When the confining pressure increases, the contact force of the particles also increases. The confining pressure can restrain the motion of the particle system and increase the dynamic strength of the sample. When the confining pressure is held constant, an increase in compressive strain causes minimal change in the contact force between soil particles. However, the contact force between the EPS particles decreases, and their displacement direction points vertically toward the center of the sample. Under an increase in compressive strain, the velocity direction of the particle system changes from a random distribution and points vertically toward the center of the sample. When the compressive strain is 5%, the number of particles deflected in the particle velocity direction increases significantly, and the cumulative rate of deformation in the lightweight soil accelerates. Therefore, it is feasible to use 5% compressive strain as the dynamic strength standard for lightweight soil. Discrete element methods provide a new approach toward the dynamic performance evaluation of lightweight soil subgrades.
... The well-known lðIÞ rheology model was proposed to describe the granular flows in the intermediate regime [26]. This model has been verified for various configurations [12,21,24,27,29,52,53,65]. This model was also extended to consider the ''shearing dilation'' behavior caused by particle collisions [5,55]. ...
... Based on the framework of Eqs. (23)(24)(25), several hypoplastic models have been developed [7,23,37,41,60]. The following applications show the capability of hypoplastic model in predicting the behavior of granular materials [17,33,49,50,56,66]. ...
We propose a constitutive model for both the solid-like and fluid-like behavior of granular materials by decomposing the stress tensor into quasi-static and collisional components. A hypoplastic model is adopted for the solid-like behavior in the quasi-static regime, while the viscous and dilatant behavior in the fluid-like regime is represented by a modified μ(I) rheology model. This model effectively captures the transition between solid-like and fluid-like flows. Performance and validation of the proposed model are demonstrated through numerical simulations of element tests.
... Representative examples in geomechanics are interactions between soils and various kinds of "structures" such as foundations, penetrometers, and machines (e.g., refs. [11][12][13][14][15][16][17][18][19][20][21][22][23]). In these problems, the displacement fields around the soil-structure interfaces usually exhibit sharp gradients due to contact between soft and stiff materials. ...
... For more details about the contact force calculation, we refer to refs. [20,23]. ...
... The footing is treated as a rigid object, being coupled with the MPM domain with a barrier contact algorithm. 20,23 For the mapped MPM discretization, we construct a map with an effective radius of map = 5 m to concentrate computational resources near the footing boundary where a sharp gradient exists. Figure 9 depicts the background grids in the physical and parametric domains, respectively. ...
The material point method (MPM) is often applied to large deformation problems that involve sharp gradients in the solution field. Representative examples in geomechanics are interactions between soils and various “structures” such as foundations, penetrometers, and machines, where the displacement fields exhibit sharp gradients around the soil‐structure interfaces. Such sharp gradients should be captured properly in the MPM discretization to ensure that the numerical solution is sufficiently accurate. In the MPM literature, several types of locally refined discretizations have been developed and used for this purpose. However, these local refinement schemes are not only quite complicated but also restricted to certain types of basis functions or update schemes. In this work, we propose a new MPM formulation, called the mapped MPM, that can efficiently capture sharp gradients with a uniform background grid compatible with every standard MPM basis function and scheme. The mapped MPM is built on the method of auxiliary mapping that reparameterizes the given problem in a different domain whereby sharp gradients become much smoother. Because the reparameterized problem is free of undesirably sharp gradients, it can be well solved with the standard MPM ingredients including a uniform background grid. We verify and demonstrate the mapped MPM through several numerical examples, with particular attention to soil‐structure interaction problems.
... To couple a material point and a rigid object, we build on the approach recently developed in Jiang et al. (2022). When the distance between a material point and a rigid object is lower than a certain value, the coupling force between the material point and the object is calculated based on a contact mechanics model. ...
... where , is the magnitude of the normal coupling force, is a parameter controlling the stiffness of the barrier model, and is the maximum distance where the coupling force is nonzero. As in Jiang et al. (2022), we assume that each material point has a spherical volume and determine as the radius of the volume. Alternatively, one may assume that the material point's volume is cubic and calculate accordingly. ...
... For the plastic behavior, we use the ( ) rheology (Jop et al., 2006), which is a rate-dependent rheology model widely used for dry granular flows. The model parameters are adopted from Jiang et al. (2022) where the same constitutive model is used to simulate granular impact experiments with the MPM. The ( ) rheology parameters adopted are as follows: the lowest friction angle min = 30 o , the highest friction angle max = 34 o , the reference inertia parameter 0 = 0.278, and the mean particle size = 0.25 mm. ...
The material point method (MPM) is often used to simulate soils that interact with (nearly) rigid objects, such as structures, machines, or rocks. Yet MPM simulations of such problems are quite challenging when the objects have complex shapes. In this paper, we propose an efficient approach for incorporating geometrically complex rigid objects into MPM modeling. The proposed approach leverages the level set method, which can efficiently delineate arbitrary surface geometry, to represent the boundary of a discrete object. For coupling the level set object with the MPM domain, a robust algorithm is developed on the basis of contact mechanics. Through numerical examples of varied complexity, we verify the proposed approach and demonstrate its ability to efficiently simulate challenging problems wherein soils interact with complex rigid objects such as debris-resisting baffles, a vehicle wheel, and basal terrain.
... The erodible soil bed is considered a continuum because its grains are much smaller than the glass beads. Previous studies (e.g., Dunatunga & Kamrin 2015;Cui et al., 2021;Jiang et al., 2022) have shown that dry sand subjected to dynamic impact can be well simulated by a continuum model that distinguishes among the following three states: elastic, plastic, and gasified. In this work, the elastic state is considered with Hencky elasticity, which is an extension of linear elasticity to accommodate geometric nonlinearity. ...
... The continuum soil bed (discretized by MPM) and the discrete granular flow (modeled by DEM) are coupled through the algorithm proposed by Jiang et al. (2022). In this algorithm, each material point is assigned a radius and checked whether it is overlapped by a discrete element. ...
... (6) Also, the P2G transfer in the MPM is modified to account for the trans-phase relation. The reader is referred to Jiang et al. (2022) for more details of the formulation and coupling algorithm. ...
Collision‐induced stresses on soil beds under granular geophysical flows have been demonstrated to be highly erosive. However, it remains mostly elusive as to how a collisional granular flow erodes and transports soil bed material. This paper presents a combined experimental and numerical investigation into the mechanisms underlying collision‐induced erosion and transport of dry soil beds. A series of flume experiments are conducted where collisional granular flows erode dry sand beds under varied conditions. The experiments are then back‐analyzed using a hybrid continuum–discrete simulator to gain physical insight into the erosion and transport processes. Results show that the key mechanism of collision‐induced erosion and transport is the retexturing of the soil bed surface. This implies that bed morphology, which has often been overlooked in mobility and hazard assessments, has profound effects on erosion and transport potential. Further, contrary to most existing models that assume all the eroded bed volume is carried away by granular flow, it is found that only up to 80% of the eroded material is transported. Also found is that the collisional stresses of the monodisperse grains in this study follow the Pareto distribution in which 80% of differences in the outcomes are due to 20% of causes. This finding suggests that there is measurable certainness in a seemingly random process of coarse grain collisions with an erodible soil bed.
... Note that the footing is treated explicitly as a rigid body. We treat the contact between the footing and the ground with a barrier method, [45][46][47][48] which guarantees non-interpenetration between the two objects. The particular barrier method implemented in this example is based on the formulation tailored to material points in contact with a discrete object. ...
... The particular barrier method implemented in this example is based on the formulation tailored to material points in contact with a discrete object. 48 The friction coefficient in the contact model is set to be sufficiently large to prevent a slip between the footing and the ground. The elastoplastic behavior of the ground is described by a combination of Hencky elasticity and J2 plasticity. ...
The material point method (MPM) is frequently used to simulate large deformations of nearly incompressible materials such as water, rubber, and undrained porous media. However, MPM solutions to nearly incompressible materials are susceptible to volumetric locking, that is, overly stiff behavior with erroneous strain and stress fields. While several approaches have been devised to mitigate volumetric locking in the MPM, they require significant modifications of the existing MPM machinery, often tailored to certain basis functions or material types. In this work, we propose a locking‐mitigation approach featuring an unprecedented combination of simplicity, efficacy, and generality for a family of explicit MPM formulations. The approach combines the assumed deformation gradient () method with a volume‐averaging operation built on the standard particle–grid transfer scheme in the MPM. Upon explicit time integration, this combination yields a new and simple algorithm for updating the deformation gradient, preserving all other MPM procedures. The proposed approach is thus easy to implement, low‐cost, and compatible with the existing machinery in the MPM. Through various types of nearly incompressible problems in solid and fluid mechanics, we verify that the proposed approach efficiently circumvents volumetric locking in the explicit MPM, regardless of the basis functions and material types.
... More specifically, the microscopic mechanism at the grain level can be obtained by the DEM, and the macroscopic mechanical behaviour can be obtained by continuous methods such as SPH and MPM. Secondly, MPM-DEM mixed simulations Yue et al., 2018;Chen et al., 2021;Jiang et al., 2022;Ren et al., 2022, Singer et al., 2022, where DEM particles and MPM particles are basically placed in a unified framework, but representing different materials, which may differ in particle sizes or properties, e.g., rocks and soils. Some simulations of debris flows have been attempted using the SPH-DEM method (Trujillo-Vela et al., 2020;Luo et al., 2022). ...
... Together with a filter-line-search scheme based on continuous collision detection (CCD), IPC guarantees global convergence and non-penetration for solids with arbitrary codimensional geometries [31] and deformation. More subsequent works have shown the formulation's versatility towards solving problems in reduced simulation of deformable [32] and rigid objects [33], [34], articulated multibody dynamics [35], projective dynamics [36], simulating viscoelastic and elastoplastic solids [7], frictional contact between embedded interfaces [37], and coupling between different spatial discretizations [38], [39]. In addition to physical simulations, barrier methods were also adopted in geometry processing to guarantee injectivity. ...
We introduce a variational formulation for simulating sticky interactions between elastoplastic solids. Our method brings a wider range of material behaviors into the reach of the Incremental Potential Contact (IPC) solver recently developed by [1]. Extending IPC requires several contributions. We first augment IPC with the classical Raous-Cangemi-Cocou (RCC) adhesion model. This allows us to robustly simulate the sticky interactions between arbitrary codimensional-0, 1, and 2 geometries. To enable user-friendly practical adoptions of our method, we further introduce a physically parametrized, easily controllable normal adhesion formulation based on the
unsigned distance
, which is fully compatible with IPC's barrier formulation. Furthermore, we propose a smoothly clamped tangential adhesion model that naturally models intricate behaviors including debonding. Lastly, we perform benchmark studies comparing our method with the classical models as well as real-world experimental results to demonstrate the efficacy of our method.
