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 one 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 key numerical tasks in multimaterial mode MPM are:

Detection of Contact

The first step is to decide if the materials at the node are in contact. This decision has to made only from extrapolated velocity field information.

Adjust Nodal Momenta or Forces

If a node is not in contact, no changes are needed. But, for nodes in contact, the nodal momenta and/or forces for each velocity field have to be adjusted to reflect the contact mechanics. Currently, NairnMPM can use multimaterial mode to model frictional contact or imperfect interfaces.

Evaluation of Surface Normals

Both the above tasks need to know the normal vector to the contacting surface. The evaluation of these normals is crucial component of multimaterial mode MPM.

The general principles of multimaterial MPM are described in Bardenhagen et al. (2001). Some improved options for detecting contact by displacements and for finding normals are unique to NairnMPM and are described in Lemiale et al. (2010) and Nairn (2013). The latter reference also describes use of multimaterial mode MPM to model imperfect interfaces between materials.

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)
(commands to set default contact properties)

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

<MultiMaterialMode Vmin='(Vmin)' Dcheck='(dispCheck)' Normals='(normals)' RigidBias='(rigidBias)'>
  <ContactPosition>(cutoff)</ContactPosition>
  (commands to set default contact properties)
</MultiMaterialMode>

The settings are:

• (Vmin) - the minimum volume required for detection of contact. It is nodal volume relative to background cell volume and therefore dimensionless. 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 of normal vectors. The options are as follows (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 (avggrad is the default normals 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. This approach is the original one used in multimaterial contact, but no longer recommended. It is available for research comparisons.
• (cuttoff) - the optional parameter sets the displacement cutoff (relative to cell size) used to detect of contact. This parameter is usually either omitted or set to 0.8.
• (commands to set default contact properties) - set default friction or imperfect interfaces properties for multimaterial contact. Note that when more than two materials are present, you can use material properties for friction and interface to override the default settings and hereby set custom contact between and specific pair of materials.