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 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 usually 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 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)
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
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).