Energy Conservation Error in the Material Point Method for Solid Mechanics

By Scott Bardenhagen. 2002

198 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/4db5191c19dfc49df8aac9074f584ff32a85005d

How researchers see this paper

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

In Computational Mechanics

1. Issam K. J. al Kafaji
2. J. Nairn
3. Alireza Sadeghirad
4. Rebecca M. Brannon
5. James Guilkey
6. J. Burghardt
7. Zhen Chen
8. Martin Berzins

In Mechanics of Materials

1. Issam K. J. al Kafaji
2. J. Nairn
3. Alireza Sadeghirad
4. Rebecca M. Brannon
5. J. Burghardt
6. James Guilkey
7. Martin Berzins
8. Michael Steffen

Citations in the corpus

• A High Order Material Point Method (2017, background): “A variant of the first benchmark has been treated in [13].”
• Formulation of a dynamic material point method (MPM) for geomechanical problems (2013, methodology): “Bardenhagen [6] showed that the original MPM algorithm by Sulsky et al.”
• A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations (2011, methodology): “The algorithm described here is the ‘update stress last (USL)’ version of the GIMP algorithm described by Bardenhagen [17].”
• A COUPLED MPM-FDM ANALYSIS METHOD FOR MULTI-PHASE ELASTO-PLASTIC SOILS (2010, methodology): “The numerical stability and the discretization scheme for the MPM have also been studied and improved (e.g., Sulsky et al., 1995; Bardenhagen, 2002; Nairn, 2003; Bardenhagen and Kober, 2004).”
• Examination and Analysis of Implementation Choices within the Material Point Method (MPM) (2008, methodology): “As Bardenhagen and Kober (2004) described in the development of GIMP, lack of regularity in ∇φ is conjectured to be the root cause of what is referred to as “grid cell crossing instabilities”. As can be seen in Fig. 2(a), piecewise-linear basis functions are only C0 continuous at cell boundaries. Tr”
• Decoupling and balancing of space and time errors in the material point method (MPM) (2010, methodology): “Balancing space and time errors Temporal convergence studies so far have not demonstrated second-order convergence as we would expect [7, 17].”
• Material Point Method Calculations with Explicit Cracks (2003, methodology): “Once a crack node withVsep Vrel Vcontact is found, the velocities above and below the crack are calculated from vki,a = pki,a mDki,a vki,b = pki,b mDki,b (11) wherea andb indicate the velocity fields corresponding to particles above and below the crack.”
• Second‐order convected particle domain interpolation (CPDI2) with enrichment for weak discontinuities at material interfaces (2013, methodology): “In the remainder of this section, common formulations of MPM-GIMP methods are presented on the basis of the ‘update stress last’ algorithm described by Bardenhagen [20].”
• An Improved Contact Algorithm for the Material Point Method and Application to Stress Propagation in Granular Material (2001, methodology): “Versions of hyperelasticity, hypoelasticity, plasticity and viscoelasticity have been implemented, Sulsky, Chen, and Schreyer (1994); Sulsky, Zhou, and Schreyer (1995); Sulsky and Schreyer (1996); Bardenhagen, Brackbill, and Sulsky (2000b); Bardenhagen and Brackbill (1998); Bardenhagen, Harstad, Mau”