Stress singularity

Why the peak keeps rising#

A linear-elastic model can assign a finite force to a mathematical point or leave a re-entrant corner with zero radius. The theoretical stress at that ideal location is unbounded. Smaller elements sample closer to it, so the finite element peak increases rather than approaching a stable physical value.

Ansys lists point loads, single-node restraints, sharp CAD corners, and linear-elastic assumptions among common simplifications that can create singular behaviour. NAFEMS gives the same warning for a critical internal corner with no modelled radius.

Singularity versus stress concentration#

A physical notch or fillet creates a high but finite stress concentration when its geometry and material behaviour are represented correctly. A singularity is different: the idealised peak has no finite elastic limit.

The distinction is tested with mesh refinement. Stress around a resolved physical radius should approach a stable value. Stress at a singular point continues to rise, even when displacements and stresses farther away have converged.

How it is handled#

The analyst can represent the physical load area or minimum radius, refine a local submodel, evaluate stress at a justified distance from the singular point, use an applicable stress-linearisation or structural-stress method, or introduce material nonlinearity when yielding belongs in the problem. The choice depends on the failure mode and governing design method.

A local singularity does not automatically invalidate every model result. It does invalidate presenting that unconverged peak as a physical material stress without explaining the idealisation and assessment method.