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.

The numerical 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. NairnMPM allows a simulation to use various combinations of the following three contact detection criteria:

If the total volume at the node is less than some fraction 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 with materials will have volume greater than zero).
Next, the normal to the material contact surface is calculated and it is used to determine the velocity of approach for the two material 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, NairnMPM can use multimaterial mode to model frictional contact, stick contact, or imperfect interfaces.

Evaluation of Surface Normals

The surface normals are needed for both the above tasks. Their calculation is crucial component of multimaterial mode MPM.

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 customized with the following commands:

MultimaterialMode (Vmin),(dispCheck),(normals),(rigidBias)
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)'>
  <ContactPosition>(cutoff)</ContactPosition>
</MultiMaterialMode>

The settings are:

(Vmin) - the minimum volume required for possible contact. Enter a number from 0 to 1. Any node with volume below that value will be modeled as not in contact. Nodes with higher volume might be in contact depending on other contact criteria. The default is 0.0.
(dispCheck) - enter enabled (or yes or 1) to enable displacement criterion for detecting contact. Enter disabled (or no or 0) to skip this check. XML files must use the numeric setting. The default is disabled (or 0).
(normals) - the method for calculation normal vectors. The options are (XML files must use numeric value):
- maxgrad (or 0) - the normal is found from the one material at the node that has the largest magnitude of its volume gradient.
- maxvol (or 1) - the normal is found from the one material at the node that has the largest magnitude of its volume.
- avggrad (or 2) - the normal is found from the volume-weighted mean volume gradient. When contact is all non-rigid materials, it averages the gradient of one material with the net gradient of all other materials. When a rigid material is involved, it averages each material with the one rigid material (this is the default option).
- owngrad (or 3) - each material uses its own normal. In contact or interface calculations, the calculations are done separately for the two sides for the surface. If the normals are not equal and opposite, this method (unlike the other three) will not conserve momentum. It is the method originally proposed in MPM contact methods (e.g., Bardenhagen, et al. (2001)), before the importance of the normal was better appreciated.
(cuttoff) - contact position

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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