Failure, Damage & Element Erosion
Distinguishing physical failure from numerical element deletion, why deleting an element is not the same as creating a crack, and why a result that changes with element size may be predicting the mesh rather than the structure.
Physical failure and numerical deletion are not the same thing
Explicit impact models represent material failure by a combination of a failure criterion, a damage initiation rule, a damage evolution law, and an element deletion or erosion rule. It is essential to keep two ideas distinct. Physical failure is the process by which a material loses its load-carrying capacity through damage accumulation, micro-cracking, void growth, shear localisation or fracture. Numerical erosion is the act of removing an element from the model when a criterion is met. The two are related — erosion is used to mimic the consequence of physical failure — but they are not identical. An element can be deleted because it is distorted beyond a numerical limit without representing a physical crack, and a physical crack can propagate through a region without any single element being deleted if the mesh is too coarse to resolve it. Treating erosion as fracture by another name hides this distinction and can produce conclusions that are numerically convenient but physically unjustified.
DELETING AN ELEMENT DOES NOT AUTOMATICALLY REPRESENT THE PHYSICAL CREATION OF A CRACK.
The failure modelling chain
A defensible failure model follows a chain. A failure criterion defines the condition at which damage begins — a critical equivalent plastic strain, a stress triaxiality-dependent fracture locus, a maximum principal stress or strain, or a coupled damage initiation surface. Damage evolution describes how the stiffness and strength of the material degrade as damage accumulates from initiation to complete loss of load-carrying capacity. Element erosion removes elements that have reached a terminal damage state or a geometric distortion limit, so that the calculation can continue without the numerical catastrophe of an inverted or zero-volume element. Each link in this chain has a physical meaning and a numerical consequence, and each must be justified by data and verified by the energy balance.
Two parallel paths through failure modelling.
PATH 1 — PHYSICAL
Physical material
→ damage initiation (criterion met: strain, stress triaxiality, etc.)
→ damage evolution (stiffness and strength degrade progressively)
→ loss of load-carrying capacity (physical crack / fracture surface)
PATH 2 — NUMERICAL
Numerical element
→ distortion / failure criterion met in the element
→ deletion (erosion) of the element from the model
These are related modelling concepts, but not identical physical processes. Erosion mimics the consequence of failure; it does not guarantee that a physical crack has been represented.Why erosion is used
Element erosion is used for several reasons, some physical and some numerical. Physically, erosion allows the model to represent material separation — a panel that tears, a projectile that perforates, a casing that ruptures — by removing material that has lost integrity. Numerically, erosion preserves robustness by removing elements that have distorted so severely that their strain and stress measures are no longer meaningful, which would otherwise halt the calculation or produce non-physical energy. In both cases the criterion that triggers erosion must be chosen with care: a criterion that is too aggressive deletes material before physical failure has occurred, understating the structure's capacity; a criterion that is too lenient allows distorted elements to persist and corrupt the solution. The criterion is a modelling decision with physical and numerical consequences, not a default to be accepted.
Energy, mesh dependence and regularisation
When an element is deleted, the internal energy it carried at the moment of deletion is removed from the model. That energy should correspond to a physical energy mechanism — the creation of fracture surface, the dissipation of damage — and it should be tracked in the energy balance. If the deleted energy simply disappears, the model is not conserving energy in a way that can be audited. A further problem is mesh dependence. Many failure criteria are based on a critical strain reached at an integration point; when that strain localises into a band one element wide, the energy dissipated in "failure" scales with the element size, and the predicted failure load changes with the mesh. A finer mesh predicts failure at a lower load because the localisation band dissipates less total energy. This is not a physical effect; it is a numerical artefact. Fracture-energy regularisation — scaling the failure strain or the damage evolution so that the energy dissipated per unit area of crack is constant regardless of element size — is one way to control this dependence, and its suitability depends on the solver, the material and the failure mechanism being represented.
IF THE FAILURE RESULT CHANGES DRAMATICALLY WITH ELEMENT SIZE, THE MODEL MAY BE PREDICTING THE MESH RATHER THAN THE STRUCTURE.
Physical failure versus numerical erosion
The table makes the distinction explicit. Keeping these two ideas separate is the foundation of a defensible failure model.
| Aspect | Physical failure | Numerical erosion |
|---|---|---|
| What it represents | Loss of material integrity through damage, cracking or fracture | Removal of an element from the calculation |
| Trigger | A physical criterion: critical strain, stress state, damage accumulation | A numerical rule: terminal damage, geometric distortion, minimum element quality |
| Consequence | A crack or fracture surface forms; load is redistributed | The element no longer contributes stiffness, mass or load path |
| Energy treatment | Energy dissipated in creating fracture surface and damage | Internal energy at deletion removed from the model and should be tracked |
| Mesh dependence | Physical; the crack path and energy are independent of mesh (in reality) | Often mesh-dependent unless the failure criterion is regularised |
| Physical meaning | A real event that can be observed and measured | A numerical artefact that mimics the consequence of failure |
Tracking the energy of deleted material
Because deleted material carries energy away from the model, the energy removed by erosion should be reported as part of the energy balance and should be explainable as a physical energy mechanism. If the deleted energy is a large fraction of the initial kinetic energy, the analyst must be confident that it represents genuine dissipation in fracture and damage rather than numerical loss. If the deleted energy is large and the physical fracture surface area is small, the model may be over-deleting material; if it is small and the structure is visibly torn, the model may be under-representing the fracture energy. The energy balance is the auditor that connects the numerical deletion back to the physical event.
The energy removed by deleted elements should be tracked and should be explainable as a physical energy mechanism — not simply disappearing.
A practical verification stance
A practical stance toward failure and erosion is to treat the erosion criterion as a parameter to be studied, not a default. Run the analysis with at least two mesh densities and confirm that the failure mode and the engineering conclusion are stable. Examine the deleted energy in the energy balance and confirm it is explainable. Compare the predicted failure mode against physical test evidence wherever possible. If the result changes with mesh, apply regularisation or acknowledge the limitation explicitly. The goal is not to produce a dramatic animation of tearing material but to produce a failure prediction that is supported by data, stable under mesh refinement and consistent with the energy balance.