Locking, Hourglassing and Element Pathologies
Recognising and avoiding the common numerical pathologies of finite elements: shear locking, volumetric locking, hourglassing and their causes.
Principle
Element pathologies produce results that are numerically converged but physically wrong. The analyst must recognise when an element formulation is inappropriate for the loading and choose an alternative or a corrective technique.
Why it matters
Shear locking makes a beam or shell model artificially stiff in bending — displacements and stresses are both underestimated. Volumetric locking occurs in nearly incompressible materials (rubber, plasticity with v → 0.5). Hourglassing produces zero-energy deformation modes that look like real deformation but involve no strain energy. All three produce plausible-looking but incorrect results.
Good practice
| Pathology | Cause | Symptom | Remedy |
|---|---|---|---|
| Shear locking | First-order full-integration elements in bending | Displacement too small (stiff) | Use reduced integration or second-order elements |
| Volumetric locking | Full integration with near-incompressible material | Excessive pressure stiffness | Use hybrid elements (C3D8H) or reduced integration |
| Hourglassing | Reduced-integration elements with insufficient control | Zigzag deformation pattern, zero energy | Use hourglass control or refine mesh |
| Membrane locking | Curved shell elements with bending | Artificial membrane stiffness | Use second-order shells (S8R) or refine |
Warning signs
- Displacements are significantly smaller than a hand calculation predicts — suspect locking
- Hourglass deformation patterns visible in the deformed shape — zigzag or chevron patterns
- Artificial strain energy is a significant fraction of total strain energy (check in explicit dynamics)
- The model is much stiffer than expected despite a fine mesh
Verification checks
- Compare displacement with a hand calculation or analytical solution for the same geometry
- Check the ratio of artificial energy to internal energy (should be < 5%)
- Refine the mesh — if the result changes dramatically, suspect a formulation problem
- Switch element type and compare results