Smoothing algorithm for stabilization of the material point method for fluid–solid interaction problems

Yang, Wen-Chia; Arduino, Pedro; Miller, Gregory R.; Mackenzie‐Helnwein, Peter

doi:10.1016/j.cma.2018.04.041

Cited by 27 publications

(14 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Despite its robustness and ease of implementation, MPM is known to develop errors that can produce spurious material flows 51 . In this work, we seek to examine and reduce these errors, with a particular focus on simulations involving extreme shear deformations of the continuum material.…”

Section: Theorymentioning

confidence: 99%

“…In this analysis, we use the standard, bi‐linear basis functions integrated using uGIMP; bi‐quadratic B‐spline basis functions 53 integrated with one‐point quadrature; or bi‐cubic B‐spline basis functions 53 integrated with one‐point quadrature. To avoid the issues associated with kinematic locking and strain‐based instabilities common to many MPM frameworks, we implement a cell‐based stabilization and anti‐locking algorithm 51 for this problem. This algorithm is discussed further in the Appendix.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Smoothing algorithms and reduced quadrature methods commonly used in FEM have been shown to overcome this locking phenomenon. However, these approaches compound the latter issue producing an unfortunate type of error: aggregation of material point tracers and loss of accurate integration of the governing equations 51 …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Baumgarten

Kamrin

2023

Numerical Meth Engineering

View full text Add to dashboard Cite

The 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.

show abstract

Section: Theorymentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

See 1 more Smart Citation

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

Baumgarten

Kamrin

2023

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…A key advantage of MPM is that it naturally captures Lagrangian flow features by using persistent material point tracers while solving the equations of motion on a temporary Eulerian grid. Despite its proven robustness in modeling many solid-like materials through large deformations, MPM is known to develop substantial integration errors when these deformations continue to grow, as occurs with pure fluids and mixtures with negligible solid volume fractions; these quadrature errors increase the rate of overall error growth during a simulation, limiting the use of MPM for long-duration fluid problems (see [34,35,36,37,38]). Although substantial work has been done to reduce these errors in MPM (see [39,40,41,42,43,44,45]), it is desirable to avoid them completely where possible.…”

Section: Introductionmentioning

confidence: 99%

A coupled finite volume and material point method for two-phase simulation of liquid-sediment and gas-sediment flows

Baumgarten,

Couchman,

Kamrin

2020

Preprint

View full text Add to dashboard Cite

Mixtures of fluids and granular sediments play an important role in many industrial, geotechnical, and aerospace engineering problems, from waste management and transportation (liquid-sediment mixtures) to dust kick-up below helicopter rotors (gas-sediment mixtures). These mixed flows often involve bulk motion of hundreds of billions of individual sediment particles and can contain both highly turbulent regions and static, non-flowing regions. This breadth of phenomena necessitates the use of continuum simulation methods, such as the material point method (MPM), which can accurately capture these large deformations while also tracking the Lagrangian features of the flow (e.g. the granular surface, elastic stress, etc.).Recent works using two-phase MPM frameworks to simulate these mixtures have shown substantial promise; however, these approaches are hindered by the numerical limitations of MPM when simulating pure fluids. In addition to the well-known particle ringing instability and difficulty defining inflow/outflow boundary conditions, MPM has a tendency to accumulate quadrature errors as materials deform, increasing the rate of overall error growth as simulations progress. In this work, we present an improved, two-phase continuum simulation framework that uses the finite volume method (FVM) to solve the fluid phase equations of motion and MPM to solve the solid phase equations of motion, substantially reducing the effect of these errors and providing better accuracy and stability for long-duration simulations of these mixtures.

show abstract

“…See [120] for an application of this capability, where oscillations due to excess of pore water pressure in consolidation problems are smoothed out by using this technique. The employment of smoothing algorithms is also straightforward in the fluid-solid interaction problems [169]. This behaviour was noticed previously by [8], were authors highlighted how, by adjusting the spatial variation of β(x), it is possible to select regions of the domain of analysis which are treated by finite elements and regions that are treated in the style of meshfree methods, with seamless transitions between those regions.…”

Section: Local Max-ent Approximantsmentioning

confidence: 79%

The Local Maximum-Entropy Material Point Method

Pérez¹

View full text Add to dashboard Cite

En este trabajo se propone el uso de una metodología B-free (o sin componentes) para la resolución de problemas de elastodinámica no lineal en grandes deformaciones mediante el LME-MPM. Esta metodología permite eliminar la brecha existente entre la formulación continua del problema y su versión discretizada. Asimismo, en este trabajo se introduce el uso de una formulación incremental del algoritmo Newmark-β para el LME-MPM. En aras de la exhaustividad, al final de este documento se analiza la evaluación del marco propuesto en el régimen de grandes deformaciones.

show abstract

Smoothing algorithm for stabilization of the material point method for fluid–solid interaction problems

Cited by 27 publications

References 10 publications

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

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

A coupled finite volume and material point method for two-phase simulation of liquid-sediment and gas-sediment flows

The Local Maximum-Entropy Material Point Method

Contact Info

Product

Resources

About