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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...
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... this end, we simulate the problem of a strip footing on an incompressible elastoplastic solid, for which an analytical solution for the bearing capacity-the Prandtl solution-is available. Figure 7 depicts the specific geometry and boundary conditions simulated herein. As shown in the figure, only the right half of the problem is modeled taking advantage of symmetry. ...
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... Numerical Schemes 254 We modify the B-Spline F-Bar volumetric antilocking scheme by Zhao et al. 2023 to use a linear mixing ratio, ∈ [0, 1], for an adjustable balance of pressure field smoothness and low-dissipation stabilization. This linear combination of B-Spline F-Bar in an explicit MPM appears in Bonus 2023 with additional exposition. ...
We present an international comparative analysis of simulated 3D tsunami debris hazards, applying three state-of-the-art numerical methods: the Material Point Method (MPM, ClaymoreUW, multi-GPU), Smoothed Particle Hydrodynamics (SPH, DualSPHysics, GPU), and Eulerian grid-based computational fluid dynamics (Simcenter STAR-CCM+, multi-CPU / GPU). Three teams, two from the United States and one from Germany, apply their unique expertise to shed light on the state of advanced tsunami debris modeling in both open source and professional software. A mutually accepted and meaningful benchmark is set as 1:40 Froude scale model experiments of shipping containers mobilized into and amidst a port setting with simplified and generic structures, closely related to the seminal Tohoku 2011 tsunami case histories which majorly affected seaports. A sophisticated wave flume at Waseda University in Tokyo, Japan, hosted the experiments as reported by \citeNP{Goseberg2016}. Across dozens of trials, an elongated vacuum-chamber wave surges and spills over a generic harbor apron, mobilizing 3--6 hollow debris -modeling sea containers-, in 1--2 vertical layers against friction. One to two rows of 5 square obstacles are placed upstream or downstream of the debris, with widths and gaps of 0.66x and 2.2x of debris length, respectively. The work reports and compares results on the long wave generation from a vacuum-controlled tsunami wave maker, longitudinal displacement of debris forward and back, lateral spreading angle of debris, interactions of stacked debris, and impact forces measured with debris accelerometers and/or obstacle load-cells. Each team writes a foreword on their digital twin model, which are all open-sourced. Then, preliminary statistical analysis contrasts simulations originating off different numerical methods, and simulations with experiments. Afterward, team's give value propositions for their numerical tool. Finally, a transparent cross-interrogation of results highlights the strengths of each respective method.
... We observe that, for even this simple case, accurate fluid pressure fields beyond one seconds requires an anti-locking scheme in MLS-MPM, though wall forces may not. The simple F-Bar scheme byZhao et al. 2023 was found to be a suitable and computationally expedient tool and ASFLIP was determined to not be necessary for ...
... A weakly-compressible fluid models was used in our simulation. We achieved good behavior using just a basic advection modification by Fei et al. 2021 and simple volumetric antilocking byZhao et al. 2023. It is especially promising that our approach can produce accurate FSI results at large computational magnitudes, tested up-to a billion particles over a million time-steps, and at length scales in the range of wave-flume tests and real world waterborne hazards.Debris-fluid interaction (DFI) results in Sec. 10 demonstrate that our numerical DFSI approach captures the debris-fluid interaction (DFI) of laminar flow around debris and the overall force balance of the buoyant, drag-laden, gravity-loaded system. ...
The study of debris-fluid-structure interaction (DFSI) poses challenges for engineers and animators alike due to its complex nature involving multiple materials, multiple phases, constitutive nonlinearity, and large deformations across varying scales. Current numerical methods frequently overlook critical aspects of DFSI, can be overly complicated to implement, and require excessive computational resources for practical applications. To alleviate this problem, this paper introduces a flexible and explicit Material Point Method (MPM) that achieves a 100-fold improvement over traditional MPM formulations in terms of CPU-based computation. The key improvement results from the implementation of computer graphics techniques (MLS-MPM, APIC, ASFLIP, Simple F-Bar) and hardware (Multiple Graphics Processing Units). However, while computer graphics prioritizes qualitative realism, engineering needs quantitative accuracy. Therefore, this paper concentrates on a series of DFSI validation benchmarks using an enhanced graphics tool for engineering applications. Carefully chosen examples highlight critical aspects of DFSI. To show stability and favorability for next-generation scales, we simulate 100,000 to 1,000,000,000 particles within hours for all benchmarks. Accuracy relative to experiments, analytical equations, and alternative numerical models is demonstrated.
... grid nodes number 7, 8, 9, 12, 13, 14, 17, 18 and 19), as shown in Figure 1B. Therefore, their material point ( ) to tensor product grid nodes ( ) connectivity matrix ( 2 matrix) is [7,8,9,12,13,14,17,18,19]. Similarly, if a material point moves to the hatched external patch, its 2 matrix will be [18,19,20,23,24,25,28,29,30], as shown in Figure 1B. This 2 matrix is crucial in MPM during the communication between the material points and their related grid nodes (in BSMPM, they are tensor product grid nodes). ...
... 6 From the above illustration, the key to the F-bar approach is to determine the averaged Jacobian Δ̄in Equation (15). Departing from the research conducted by Zhao et al., 28 we calculate the averaged Jacobian Δ̄by mapping the original one Δ to the related grid nodes and then mapping back to the material points. The mathematical formulation of this mapping and remapping procedure is stated as follows: ...
... The idea of our modified F-bar Method is similar to the method proposed by Zhao et al., 28 but these are different methods because (a) we use a different incremental version of the F-bar Method; (b) we apply the mapping and re-mapping technique to the term Δ instead of and (c) we also smooth the left elastic Cauchy-Green strain. These modifications improve the algorithm's performance under extremely large deformation situations, which will be shown in the later numerical examples. ...
The Material Point Method (MPM) has drawn great attention in the numerical modelling of large deformation, geotechnical problems. The popularity of MPM is mainly because its formulation shares significant similarities with the Finite Element Method. In MPM, the iteration points can move independently from the mesh, allowing for the resolution of large deformation problems. However, because of this, the original MPM formulation suffers from the well-known cell-crossing noise and volumetric-locking instabilities, resulting in a strongly oscillated stress field. A novel implicit locking-free B-spline MPM that controls stress oscillations to a negligible level is proposed in this paper. A novel, but very straightforward B-spline shape function implementation procedure, avoids the need for a complex material point searching algorithm, providing seamless transformation from the original MPM to this robust B-spline MPM, aiming at modelling large-strain geotechnical problems. The newly proposed volumetric locking mitigation strategy is also very easy to implement, which facilitates the reproducibility of this research. The proposed method is validated against three numerical studies: granular column collapse experiment, slope failure and footing with large penetration. The proposed numerical method agrees well with experiments reported in the literature and previous numerical studies. Also, these numerical examples show that the proposed method provides a more prominent stress field than other available methodologies.
