Using Ansys Mechanical's Augmented Lagrangian Contact Solver for Better Frictional Contact Accuracy

Problem: Excessive Penetration in Frictional Contact Simulations

When simulating assemblies that slide or bolt together, a pure penalty contact formulation often allows noticeable interpenetration between surfaces. This penetration can distort stress results and hide true load paths, especially in bolted joints under shear.

Thesis: Switching to the Augmented Lagrangian contact formulation reduces penetration while keeping solve times comparable, provided the contact stiffness and tolerance are tuned appropriately.

How the Augmented Lagrangian Method Works

The augmented Lagrangian approach blends a penalty term with a Lagrange multiplier update. The penalty term enforces a approximate constraint, while the multiplier corrects the residual error each iteration. Key user‑controlled settings are:

• Contact stiffness factor – scales the base penalty stiffness; higher values drive penetration down.
• Penetration tolerance – the maximum allowable overlap before the multiplier is updated.
• Maximum iterations – limits how many multiplier updates the solver will perform.

When the penetration falls below the tolerance, the multiplier is adjusted and the penalty stiffness can be reduced, improving the conditioning of the global matrix.

Worked Example: Bolted Joint Under Shear Load

1. Create a simple two‑block geometry representing the bolt head and plate, with a cylindrical bolt shaft passing through a clearance hole.
2. Define a frictional contact pair between the bolt shank and the hole wall. In the contact properties set Contact Formulation to Augmented Lagrangian.
3. Start with a moderate stiffness factor (e.g., 0.1 times the default penalty stiffness) and a penetration tolerance of 1e-5 mm. Set the maximum iterations to 25.
4. Apply a shear displacement of 2 mm to the top plate and fix the bottom plate. Use a static structural analysis.
5. Run the solve. In the solver output look for the line Contact Residual – it should drop below the specified tolerance within the iteration limit.
6. Post‑process: query the contact penetration result. With the settings above you should observe a penetration on the order of 1e-5 mm (practically zero) and reaction forces comparable to a pure penalty run.

For comparison, repeat the same model with Contact Formulation set to Pure Penalty using the default stiffness factor. The penetration typically rises to 0.1‑0.2 mm and the solver may need more iterations to converge, increasing total solve time.

Formulation	Typical Penetration (mm)	Relative Solve Time*
Pure Penalty (default)	0.15	1.00
Augmented Lagrangian (tuned)	<0.01	0.80

*Times are illustrative based on the research brief; actual values depend on mesh size, hardware, and solver options.

Trade‑off and Limitations

Increasing the contact stiffness factor improves accuracy but can make the global stiffness matrix ill‑conditioned. This may:

• Require a more robust linear solver (e.g., Direct Sparse instead of Iterative).
• Necessitate smaller time steps in transient or explicit dynamics analyses.
• Lead to convergence difficulties if the stiffness is too high relative to the material’s bulk modulus.

Additionally, the augmented Lagrangian formulation assumes isotropic Coulomb friction. If you need anisotropic, temperature‑dependent, or user‑defined friction laws, you must fall back to a user subroutine (USERFRIC) or choose a different contact formulation.

Actionable Closing

If you notice unwanted penetration in frictional contact results, try the augmented Lagrangian formulation:

1. Switch the contact formulation to Augmented Lagrangian.
2. Begin with a low‑to‑moderate stiffness factor (0.05‑0.2 of the penalty default) and a tight penetration tolerance (1e‑5 mm).
3. Monitor the contact residual in the solver output; increase the stiffness factor only if the residual stalls above tolerance.
4. Check the conditioning warning in the solver log; if you see ill‑conditioning messages, switch to a direct solver or reduce the stiffness factor.
5. Validate by comparing penetration and reaction forces against a pure penalty baseline.

When the contact residual converges within the tolerance and the penetration is acceptably low, you have achieved a more accurate contact representation without a significant penalty in solve time.