Main Help → All Commands → MPM Analysis Header → MPMMethod
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
(strainUpdate)
is method used to update strains each time step. The options are:
USF
- update strain firstUSAVG
or USAVG+
- update strain first and last (like a midpoint rule) (the default method)USAVG-
- update strain first and last, but last is modified [4]USL
or USL+
- update stain last (SZS
is old name for this method that is still accepted)USL-
- modified [4] method to update stain last(MPMMethod)
is the shape function method. The options are:
Classic
(or Dirac
or 0) - classic MPM that uses conventional shape functions with the particle domains treated as delta functions. This method is the default if no option is specified.uGIMP
(or GIMP
or 1) - assumes the particle domain is fixed at its original size and just translates with the particle and integrates exactly over that domain.lCPDI
(or CPDI
or 2) - assumes the particle domain deforms into a parallelogram (2D) or a parallelepiped (3D) (as defined by its current deformation gradient) and then integrates over the domain using linear isoparametric shape functions with nodes at the corners of the parallelogram (2D) or parallelepiped (3D).qCPDI
(or 3) - same as lCPDI
except integrates over the domain using quadratic shape functions with 9 nodes at corners, edge midpoints, and domain center of the parallelogram (currently 2D only, slower than lCPDI, and not found to be beneficial).Finite
(or 4) - exactly integrated GIMP integrals (currently 2D only, and only in OSParticulas).B2GIMP
(or 5) - uGIMP method by based on quadratic spline grid shape functions (instead of linear ones used in uGIMP).B2SPLINE
(or 6) - Classic MPM method based on quadratic spline shape functions.B2CPDI
(or 7) - CPDI method by based on quadratic spline grid shape functions (instead of linear ones used in CPDI).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.
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.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 efficientUSL
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+
.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.uGIMP
, Finite
, B2GIMP
, B2SPLINE
, and B2CPDI
all require a regular grid (i.e., constant element size).
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.MPMMethod
command is only allowed for MPM analyses.