Multimaterial MPM

Multimaterial mode is an advanced MPM model that allows new options for modeling contact and material interfaces.

Multimaterial Mode Concepts

In multimaterial MPM, particles of each material type extrapolate to separate velocity fields on the grid. Nodes with a single material and therefore only on velocity field proceed by normal MPM methods. Nodes with velocity fields from more than one material might be in contact. If they are in contact, the nodal momenta have to be changed to represent contact physics. The various options implemented in multimaterial mode code determine the physcial phenomna that can be modeled. NairnMPM can use multimaterial model to model either frictional contact or imperfect interfaces.

The key tasks in multimaterial mode MPM are:

Detection of Contact

The first step is to decide if the materials at the node are actually in contact. This check has several options and NairnMPM allows a simulation to use some combination of the following three contact criteria:

If the total volume at the node is less than some fracture of the total volume expected for an internal node (a parameter Vmin), the materials at that node are assumed to not be in contact. If the volume is greater than Vmin, the contact detection continues. This check can be skipped by setting Vmin = 0 (because all nodes will have volume greater than zero).
Next, the normal to the surface is calculated and it is used to determine the velocity of approach for the two surfaces. If the surfaces are moving apart, the node is assumed to not be in contact. If they are moving toward each other, the contact detection continues.
Finally, if enabled, the displacements for each material at the node are calculated. If the two materials overlap, the node is in contact. If not, the node is assumed to not be in contact. There are two ways to find displacements. The method is selected with the ContactPosition command (where details on the methods are given).

Adjust Nodal Momenta or Add Internal Forces

Once contact is detected, the nodal momenta for each velocity field are adjusted to reflect the contact mechanics. Currently, the contact methods that are implemented are frictional contact, stick contact, and imperfect interfaces.

Evaluation of Surface Normals

The surface normals are needed for both the above tasks. First they are needed to find the component of the velocity in the approaching direction. Second, they are needed to implement contact mechanics. The results of multimaterial mode MPM simulations can demonstrate that accuracy of results is very sensitive to the method used to find the normal. Traditional MPM has relied on the mass gradient of each material. NairnMPM has implemented new methods that seem to work better. No one method works for all problems, but problems with multimaterial mode MPM are usually caused by inaccurate normals.

The general principles of multimaterial contact are described in Bardenhagen et al. (2001).^[1] The new options of detecting contact by displacements and finding normals by new methods are unique to NairnMPM and are described in Lemiale et al. (2010)^[2] and Nairn (2013).^[3] The latter reference also describes use of multimaterial mode MPM to model imperfect interfaces between materials.^[3]

Multimaterial Mode Input Commands

In scripted input files, multimaterial mode MPM is activated and customizes with the following commands:

MultimaterialMode (Vmin),(dispCheck),(normals),(rigidBias)
FrictionMM (frict)
ContactPosition (cutoff)
ImperfectInterfaceMM (Dt),(Dntens),(DNcomp)

In XML files, multimaterial mode MPM is activated with the following block:

<MultiMaterialMode Vmin='(Vmin)' Dcheck='(dispCheck)' Normals='(normals)' RigidBias='(rigidBias)'>
  <Friction>(frict)</Friction>
  <ContactPosition>(cutoff)</ContactPosition>
</MultiMaterialMode>

Also set material properties with Friction and Interface commands.

Next steps - write up imperfect interface elements with a separate topic on imperfect interface mechanics.

Friction

Imperfect Interfaces

Contact Position

References

↑ S. G. Bardenhagen, J. E. Guilkey, K. M. Roessig, J. U. Brackbill, W. M. Witzel, and J. C. Foster, "An Improved Contact Algorithm for the Material Point Method and Application to Stress Propagation in Granular Material," Computer Modeling in Engineering & Sciences, 2, 509-522 (2001).
↑ V. Lemiale, A. Hurmane, and J. A. Nairn, "Material Point Method Simulation of Equal Channel Angular Pressing Involving Large Plastic Strain and Contact Through Sharp Corners," Computer Modeling in Eng. & Sci., 70(1), 41-66, (2010).
↑ ^3.0 ^3.1 J.A. Nairn, "Modeling Imperfect Interfaces in the Material Point Method using Multimaterial Methods," Computer Modeling in Eng. & Sci., 92, 271-299 (2013).

[bard-1] S. G. Bardenhagen, J. E. Guilkey, K. M. Roessig, J. U. Brackbill, W. M. Witzel, and J. C. Foster, "An Improved Contact Algorithm for the Material Point Method and Application to Stress Propagation in Granular Material," Computer Modeling in Engineering & Sciences, 2, 509-522 (2001).

[Lemiale-2] V. Lemiale, A. Hurmane, and J. A. Nairn, "Material Point Method Simulation of Equal Channel Angular Pressing Involving Large Plastic Strain and Contact Through Sharp Corners," Computer Modeling in Eng. & Sci., 70(1), 41-66, (2010).

[Nairn-3] 3.0 ^3.1 J.A. Nairn, "Modeling Imperfect Interfaces in the Material Point Method using Multimaterial Methods," Computer Modeling in Eng. & Sci., 92, 271-299 (2013).

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