Examination and Analysis of Implementation Choices within the Material Point Method (MPM)

By Michael Steffen, Philip C. Wallstedt, James Guilkey, Robert Michael Kirby, Martin Berzins. 2008

126 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/848305dd6991e913bf3c2a77b68bf7f0906306ee

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Stéphane P.A. Bordas
2. Timon Rabczuk
3. Martin Berzins

In Computational Mechanics

1. Charles E. Augarde
2. Stéphane P.A. Bordas
3. Timon Rabczuk
4. William M. Coombs
5. Cosmin Anitescu
6. Vinh Phu Nguyen
7. Xiaoying Zhuang
8. T. J. Charlton

In Mechanics of Materials

1. Charles E. Augarde
2. Timon Rabczuk
3. Stéphane P.A. Bordas
4. William M. Coombs
5. Vinh Phu Nguyen
6. Xiaoying Zhuang
7. Cosmin Anitescu
8. T. J. Charlton

Citations in the corpus

• A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations (2011, background): “Also, their basic algorithms and formulations have been studied by a number of authors such as [17–29].”
• B-spline based boundary conditions in the material point method (2019, background): “Although there are no restrictions placed on the form of the background mesh, a structured grid with regular elements is often chosen due to its high computational efficiency [7].”
• Decoupling and balancing of space and time errors in the material point method (MPM) (2010, methodology): “More details regarding the use of B-spline basis functions within MPM, including boundary condition choices, are outlined in [12].”
• Second‐order convected particle domain interpolation (CPDI2) with enrichment for weak discontinuities at material interfaces (2013, background): “Some early efforts to evolve GIMP support domains with deformation allowed each p to be an axis-aligned rectangle that could change height and width, but not shape or orientation [16], again corresponding to a 0th-order accurate (and frame dependent) description of general material motion.”
• A new method for material point method particle updates that reduces noise and enhances stability (2017, background): “Other possible shape functions include CPDI [20], higher order b-splines [21], and many undeveloped ones that could be derived by GIMP methods [19].”
• Isogeometric analysis: An overview and computer implementation aspects (2012, methodology): “B-splines are used in the material point method to alleviate the cell-crossing issue [129].”