Using Augmented Lagrange Contact in Ansys Mechanical for Nonlinear Structural Analysis

Using Augmented Lagrange Contact in Ansys Mechanical

When a nonlinear structural analysis involves parts that may touch or slide, the Augmented Lagrange (AL) contact formulation helps keep penetration small while avoiding an overly stiff penalty matrix. This guide shows the essential steps, a worked configuration, and the limits to watch for.

Workflow Overview

1. Open a static structural analysis in Ansys Workbench.
2. Create or import the two bodies that will interact (e.g., a rectangular block and a flat plate).
3. Define a frictional contact connection between the bodies.
4. In the contact properties, change Contact Formulation from the default Pure Penalty to Augmented Lagrange.
5. Enter a penalty stiffness value (e.g., 1e5 N/m³) and a tolerance (e.g., 1e-3).
6. If large rotations or strains are expected, enable Large Deflection in the analysis settings.
7. Solve the model and inspect contact results.

Example Configuration

The table below shows a typical set‑up for a block‑on‑plate problem where the block is pressed onto the plate with a friction coefficient of 0.2.

Setting	Value	Notes
Contact Formulation	Augmented Lagrange	Switches from pure penalty to AL.
Penalty Stiffness	1e5 N/m³	High enough to limit penetration (<0.1% of block thickness) but not so high as to cause ill‑conditioning.
Tolerance	1e-3	Controls the Lagrange multiplier update convergence.
Friction Coefficient	0.2	Defines stick/slip behavior.
Large Deflection	On	Required for AL updates to be applied correctly in nonlinear steps.

Limits and Common Mistakes

• Penalty stiffness too low (<1e3 N/m³) leads to noticeable penetration; the solver may report large interference values.
• Penalty stiffness too high (>1e7 N/m³) can make the stiffness matrix ill‑conditioned, causing slow convergence or solver failure.
• For very soft materials (low elastic modulus) the AL method may need many iterations; consider reducing the time step or using a softer penalty.
• AL contact is not recommended for explicit dynamics; the pure penalty approach is preferred there because explicit solvers do not handle Lagrange multiplier updates well.
• Forgetting to enable Large Deflection prevents the Lagrange multiplier updates from being active, effectively falling back to pure penalty behavior.
• When friction is defined, an inappropriate stick/slip tolerance can cause the solver to oscillate between states; keep the tolerance consistent with the contact tolerance.

Verification and Practical Checks

After solving, verify that the AL settings produced acceptable results:

1. Open the Contact Tool in the results branch and check the Total Penetration value; it should be below the tolerance multiplied by a characteristic length (e.g., 0.001 * block thickness).
2. Plot contact pressure across the interface; a smooth distribution without abrupt spikes indicates the constraint is being enforced properly.
3. Compare key outputs (e.g., reaction force, displacement of the block) with a reference run that uses a very high penalty stiffness (1e8 N/m³). The values should agree within a few percent.
4. Perform a mesh refinement study (e.g., halve the element size) and confirm that the solution changes minimally, showing the formulation is not overly dependent on mesh density.

If penetration exceeds the acceptable limit, lower the penalty stiffness slightly and re‑solve; if convergence stalls, increase the stiffness or tighten the tolerance. Always document the final values used for reproducibility.