Advances in Imposing Nonconforming Neumann Boundary Conditions in the Material Point Method
Publication: Geo-Congress 2024
ABSTRACT
Due to the material point method’s hybrid Lagrangian-Eulerian formulation, both conforming and nonconforming boundaries often exist throughout a simulation. Imposing nonconforming boundary conditions in the MPM remains a challenge due to the material boundary continually updating throughout a simulation. Regardless of the computational challenges, imposing Neumann boundary conditions is vital for modeling a wide variety of geotechnical problems. Recently, two variations of the MPM, the CutMesh MPM and the virtual stress boundary (VSB) method, have been proposed for imposing nonconforming Neumann boundary conditions. The current study uses two benchmark problems to directly compare the numerical performance of these newly developed variations of the MPM. For very simple problems, the CutMesh MPM has lower error than the VSB method, but as problem geometry becomes more complex, both methods produce comparable results.
Get full access to this article
View all available purchase options and get full access to this chapter.
REFERENCES
Bardenhagen, S. G., and E. M. Kober. 2004. “The generalized interpolation material point method.” Computer Modeling in Engineering and Sciences. 5.6: 477–496.
Given, J., S. Kularathna, E. Y. S. Tjung, B. Chandra, K. Soga, H. Wang, S. P. Morgan, H. A. Meier, and J. L. Garson. 2022. “Modeling wellbore erosion using standard and cut-mesh approaches in material point method.” In Proc., Geo-Congress 2022. Reston, VA: ASCE, 618–627.
Gordon, P. A., F. Liu, H. A. Meier, R. Panchadhara, and V. Srivastava. 2019. “A material point method for simulation of viscoelastic flows.” Comp. Particle Mechanics. 6(3): 311–325.
Kumar, K., J. Salmond, S. Kularathna, C. Wilkes, E. Tjung, G. Biscontin, and K. Soga. 2019. “Scalable and modular material point method for large-scale simulations.” In Proc., 2nd Int. Conf. on the MPM for Modeling Soil Water-Structure Interaction. 262–267.
Liang, Y., J. Given, and K. Soga. 2023. “The imposition of nonconforming Neumann boundary condition in the material point method without boundary representation.” Computer methods in applied mechanics and engineering. 404. 115785.
Nicholson, J. E., and R. E. Snyder. 1982. Geothermal-well completions: a survey and technical evaluation of existing equipment and needs. Albuquerque, NM: Sandia National Labs.
Papamichos, E., I. Vardoulakis, J. Tronvoll, and A. Skjaerstein. 2001. “Volumetric sand production model and experiment.” Int. J. Numer. Anal. Meth. Geomech. 25, 789–808.
Salencon, J. 1969. “Contraction quasi-statique d’une cavite a symetrie spherique ou cylindrique dans un milieu elastoplastique.” Annales des ponts et chaussées. Vol. 4.
Setiasabda, E. Y. 2020. Material point method for large deformation modeling in geomechanics using isoparametric elements. Ph.D. dissertation, Berkeley, CA: Univ. of California, Berkeley.
Sulsky, D., Z. Chen, and H. L. Shreyer. 1994. “A particle method for history-dependent materials.” Computer methods in applied mechanics and engineering. 118(1-2), 179–196.
Yu, H. S. 2000. Cavity expansion methods in geomechanics. Spring Science & Business Media.
Information & Authors
Information
Published In
Geo-Congress 2024
Pages: 307 - 315
History
Published online: Feb 22, 2024
ASCE Technical Topics:
- Analysis (by type)
- Boundary conditions
- Boundary value problem
- Computer models
- Differential equations
- Domain boundary
- Engineering fundamentals
- Equations (by type)
- Geotechnical engineering
- Geotechnical models
- Hybrid methods
- Lagrangian functions
- Mathematical functions
- Mathematics
- Methodology (by type)
- Models (by type)
- Numerical analysis
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.