Large-Strain Kinematics
When deformations are so large that the geometry itself changes — sheet metal forming, rubber seals, biomedical devices.
1. What is it?
Large-strain kinematics handles problems where the part deforms so much that the original geometry no longer represents the physics:
- Green-Lagrange strain: E = ½(FᵀF — I) — measures strain in the deformed configuration, not the original.
- Deformation gradient F: captures both stretch and rotation.
- Polar decomposition: F = R·S — separates rotation from stretch.
- Co-rotational formulation: tracks the element's local frame as it rotates.
"This rubber seal compresses to 40% of its original height — will it seal properly?"
2. When do I use it?
| Use when | Don't use for |
|---|---|
| Strain > 5% (large deformation) | Small strains (use Static Structural) |
| Rubber, elastomers, polymers | Metals (use Nonlinear or Static) |
| Sheet metal forming | Simple bending (use Static Structural) |
| Biomedical device deformation | Vibration (use Dynamics) |
3. The flow — every action described
Step 1: Design (geometry)
What you do: Draw your part or import a CAD file.
How:
- Click Design tab
- Pick a primitive or import geometry
- Ensure the mesh is fine enough for large deformation
Why: Large-strain problems need mesh resolution to capture deformation gradients.
Step 2: Boundary (material + supports + loads)
What you do: Define material, constraints, and loading.
How:
- Click Boundary tab
- Material: Define hyperelastic or elasto-plastic constitutive law
- Supports (BCs): Fix faces/edges
- Loads: Apply displacement-controlled loading (preferred for large deformation)
Why: Displacement control is more stable than force control for large deformations.
Step 3: Mesh
What you do: Cut the part into small cells.
How:
- Click Mesh tab
- Adjust mesh size — finer than small-strain analysis
- Click Generate
Why: Large deformation gradients need resolution.
Step 4: Simulate → Large-Strain
What you do: Run the large-strain solver.
How:
- Click Simulate tab
- Select Large-Strain Kinematics
- Enable Green-Lagrange strain and co-rotational formulation
- Set number of load steps (more steps for stability)
- Click Run
Why: The solver tracks the deformed geometry and updates the stiffness matrix.
Step 5: Results
What you do: Read the deformed shape and stress.
How:
- Click Results tab
- View deformed shape — how much did it change?
- View Green-Lagrange strain — true strain measure
- View 2nd Piola-Kirchhoff stress — stress in deformed configuration
Why: The deformed shape shows the final geometry. The strain and stress are in the current configuration.
4. Reading your results
Deformed shape
| Color | Meaning |
|---|---|
| Blue | Little deformation |
| Red | Large deformation |
Good: Deformation is within functional requirements. Bad: Excessive deformation — redesign needed.
Green-Lagrange strain
| Color | Meaning |
|---|---|
| Blue | Small strain |
| Red | Large strain |
Good: Strain is within material limits. Bad: Strain exceeds material failure strain.
2nd Piola-Kirchhoff stress
| Color | Meaning |
|---|---|
| Blue | Low stress |
| Red | High stress |
Good: Stress is within material limits. Bad: Stress exceeds material strength.
5. Boundaries of truth
What's validated
| Case | Reference | Error |
|---|---|---|
| Green-Lagrange strain (uniaxial) | Exact | Machine precision |
| Polar decomposition (F = R·S) | Exact | < 1e-10 |
| Co-rotational pure shear | Analytical | < 1% |
| Neo-Hookean uniaxial stretch | Closed-form | < 2% |
What's NOT covered
- Full nonlinear B-matrix assembly — moderate strains only
- Consistent tangent for Green-Lagrange — modified Newton used
- Contact during large deformation — not yet integrated
- Fracture at large strain — no ductile damage model
- Dynamic large-strain — quasi-static only
Common mistakes
| Mistake | Fix |
|---|---|
| Too few load steps | Increase load steps for stability |
| Force control instead of displacement | Use displacement control for large deformation |
| Coarse mesh | Refine mesh — large gradients need resolution |
| Wrong constitutive law | Use hyperelastic for rubber, elasto-plastic for metals |
| Ignoring rotation | Enable co-rotational formulation |
See also
- [Static Structural](static-structural.md) — for small-strain analysis
- [Nonlinear](nonlinear.md) — for plastic deformation
- [Contact](contact.md) — for touching parts during deformation
Keep exploring
Open the interactive workspace — mesh, solve, validate and export in the browser.
Start a guided solve