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MPMMethod Command

There are several ways to update strain in each MPM time step and several options for calculating shape functions. All these options are described in the OSUPDocs wiki. The MPMMethod command is use to selection among these options:

MPMMethod (strainUpdate),<(MPMMethod)>

where

Shape Function Methods

Classic is described in original MPM papers (e.g., Sulsky, Chen and Schreyer (1994) and Sulsky, Zhou, and Schreyer (1995)). All other methods are approximations to a method known as GIMP or the generalized interpolation material point method (Bardenhagen and Kober (2004)). They find shape functions by integrating over the particle domain and differ in how they describe the domain or in how the do the integration. The CPDI methods were developed by Sadeghirad, Brannon, and Burghardt (2011). The spline methods replace linear grid shape functions with quadratic spline shape functions.

Notes

  1. USF is described by Bardenhagen (2002). It is very similar to USL but there are some minor differences that lead to differences in the results.
  2. USAVG is a method that combines the strain updating methods of and USF and USL (see Nairn 2003). It functions like a midpoint rule, is stable, and conserves energy better than the other methods. It is the recommended method for all MPM calculations, but if efficiency is crucial (e.g., for very large calculations), the USF method is the most efficient
  3. USL or USL+ is based on small revision of the original MPM algorithm (Sulsky, Chen and Schreyer (1994)). For backward compatibility, it can be selected using SZS instead of USL or USL+.
  4. The USAVG+ and USL+ methods re-extrapolate momenta to the grid and re-impose contact conditions prior to updating the strain after the momenta update. The USAVG- and USL- methods skip the second extrapolation. The method to use may depend on the problem, but some problems with contact seem to require the "+" methods. If both are equal, the "-" methods are more efficient.
  5. uGIMP, Finite, B2GIMP, B2SPLINE, and B2CPDI all require a regular grid (i.e., constant element size).
  6. If lCPDI, 2CPDI, or B2CPDI failure in parallel code because not enough ghost nodes, you can try truncating the CPDI shape functions of highly deformed particles to som critical radius.
  7. The MPMMethod command is only allowed for MPM analyses.