Mortar Method Contact
Mortar Method Contact: Theoretical Foundations
What is the Mortar Method?
Professor, is the Mortar method the latest contact technique?
The Mortar method is a technique that imposes contact conditions in weak form (integral form). It is more robust to mesh non-conformity than the traditional Node-to-Surface (NTS) contact.
Traditional NTS method: Slave nodes are projected onto the master surface. Contact conditions are evaluated as "points" at each node.
Mortar method: Contact conditions are evaluated by integrating over the entire contact surface. Constraints are satisfied in an averaged sense over the entire surface.
So the difference is whether evaluation is done at "points" or over the "surface".
Advantages of the Mortar method:
- Robust to mesh non-conformity — Master and slave meshes do not need to match
- No contact pressure oscillation — Eliminates checkerboarding that occurs with the NTS method
- Path independent — Less dependent on master/slave selection
Implementation in Abaqus
Abaqus's SURFACE TO SURFACE contact is Mortar-based. NODE TO SURFACE is the traditional NTS method.
```
*CONTACT PAIR, INTERACTION=prop, TYPE=SURFACE TO SURFACE
```
Abaqus's default is SURFACE TO SURFACE (Mortar).
Summary
Key points:
- Integrate contact conditions over the entire surface — More robust than point evaluation
- Robust to non-conforming meshes — Master/slave meshes can be different
- Abaqus's SURFACE TO SURFACE is Mortar-based — Default
- No contact pressure oscillation — Overcomes weaknesses of the NTS method
Bernardi-Maday-Patera 1993
The Mortar method was devised in 1993 by C. Bernardi, Y. Maday, and A.T. Patera for domain decomposition in the spectral element method. It ensures continuity in a weak sense via L² projection between subdomains with different meshes. Its application to contact problems was formulated by Ben Belgacem (1999), who proved that integral accuracy of contact pressure is maintained even between non-conforming meshes.
Computational Methods for Mortar Method Contact
Mortar Method Calculation
The Mortar method constructs integral segments between contact surfaces and evaluates constraints surface-to-surface.
- Abaqus: SURFACE TO SURFACE (default)
- Ansys: MPC CONTACT or Mortar contact
- Nastran: MORTAR contact (SOL 400)
So the Mortar method is available in all solvers.
Modern commercial solvers are transitioning to Mortar-based contact. The NTS method remains as legacy, but the Mortar method is recommended for new analyses.
Summary
Implementation of Segment Integration
The core of Mortar contact calculation is finding the intersection segments between master and slave surfaces and performing Gaussian integration on each segment. In the algorithm by Fischer & Wriggers (2005), 3D intersecting polygon clipping is implemented using the Sutherland-Hodgman algorithm, ensuring that integration points do not overlap even for complex curved surface contacts. This processing is one of the most geometrically heavy parts of the code.
Mortar Method Contact in Practice
Mortar Method in Practice
Using the Mortar method "by default" is best practice. There are rare reasons to explicitly choose the NTS method.
Practical Checklist
Wind Turbine Main Shaft Contact Analysis
Vestas began adopting the Mortar method around 2015 for non-conforming mesh contact between wind turbine main shafts and housings. The shaft side mesh density is locally fine around bearing grooves, while the housing side is coarse, but Mortar projection ensures load transfer at the interface exceeds 99.5% of theoretical value. With traditional tie contact (node-to-node), artificial stress concentrations occurred at non-conforming areas, leading to underestimation of fatigue life.
Mortar Method Contact: Software & Solver Comparison
Mortar Method Tools
Selection Guide
Sierra/Solid and Mortar Implementation
Sandia National Laboratories in the US implemented mortar contact in the Sierra/Solid code in V4.0 (2008) and has utilized it for component contact analysis in nuclear explosion simulations. Commercially, ABAQUS 6.14 (2014) added the mortar formulation option, opening it up for large assembly analyses with non-conforming meshes. In ANSYS Mechanical, mortar contact was promoted from preview to official feature in version 2019R1 (2019).
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