Material Failure, Damage & Element Deletion

What Is It?

Material failure, damage and element deletion are the numerical methods used in explicit FEA to represent the progressive loss of material capability under severe loading. Damage models track the degradation of material stiffness from initial damage through to complete failure. When an element reaches full failure, it is deleted — removed from the analysis — so that it no longer carries load. This allows the simulation to represent crack propagation, fragmentation, penetration and material separation. Understanding the distinction between yield, damage initiation, damage evolution, failure and element deletion is essential for credible failure analysis.

Why It Matters

Failure modelling is one of the most challenging aspects of non-linear analysis. The predicted failure mode, failure location and failure load depend strongly on the damage model, the failure parameters and the mesh. A model that predicts failure without a physically based damage model may produce results that are mesh-dependent and unreliable. Understanding how damage models work, what data they require and what their limitations are is essential for any engineer performing failure analysis. The consequences of incorrect failure prediction — over-predicting structural capability or predicting failure where none occurs — can be severe.

Element deletion is a numerical representation of material failure — not the physical failure mechanism itself. The physical mechanism is fibre breakage, matrix cracking, ductile fracture or shear banding. The model approximates this with a damage law and element removal.

Yield vs Damage Initiation vs Damage Evolution vs Failure

Ductile Damage

Ductile damage models represent the failure of ductile metals through void nucleation, growth and coalescence. The damage initiates when a criterion — typically based on equivalent plastic strain and stress triaxiality — is met. The damage then evolves as the plastic strain increases, degrading the material stiffness progressively. When the damage variable reaches 1.0, the element fails and is deleted. Ductile damage models require material data — the strain to failure as a function of stress triaxiality — which is obtained from notched tensile tests or other calibration tests.

Strain-to-Failure Approaches and Limitations

A simple failure model deletes the element when the equivalent plastic strain reaches a specified strain-to-failure value. This is easy to implement but has significant limitations. The strain-to-failure is not a constant — it depends on the stress triaxiality (the ratio of hydrostatic to deviatoric stress), the strain rate and the temperature. Using a single strain-to-failure value for all stress states can produce incorrect failure predictions. More sophisticated models use a damage initiation criterion that accounts for triaxiality, followed by damage evolution that controls the energy dissipation during failure.

COMMON MISTAKE: Using a single strain-to-failure value for all stress states. Ductile failure strain depends on stress triaxiality, strain rate and temperature. A constant value can produce incorrect failure predictions for combined stress states.

Triaxiality Dependence

Stress triaxiality — the ratio of the mean (hydrostatic) stress to the equivalent (von Mises) stress — strongly affects ductile failure. High triaxiality (e.g. at a notch or crack tip) promotes void growth and reduces the strain to failure. Low triaxiality (e.g. pure shear) suppresses void growth and increases the strain to failure. A failure model that does not account for triaxiality will predict the same failure strain at a notch (high triaxiality) and in a shear zone (low triaxiality) — which is physically incorrect. Modern ductile damage models include triaxiality dependence in the damage initiation criterion.

Composite Damage

Composite failure models are distinct from metallic ductile damage. Composites fail through multiple modes — fibre tension/compression, matrix tension/compression, shear and delamination. Composite damage models track each mode separately, degrading the appropriate stiffness components as damage accumulates in each mode. Hashin-type criteria identify the damage mode; damage evolution laws control the post-initiation behaviour. Element deletion occurs when the fibre-direction damage reaches full failure (the ply can no longer carry load in the fibre direction). Cross-linking to the Composite Structures chapter is recommended for detailed composite failure discussion.

Element Deletion and Mass/Energy Removal

When an element is deleted, its mass, internal energy and stiffness are removed from the model. This has physical and numerical implications. Physically, the deleted material represents fractured or fragmented material that is no longer connected to the structure. Numerically, the mass and energy removal must be tracked in the energy balance — the deleted mass and energy should be reported and should be small relative to the total unless significant material is being removed. If large amounts of mass or energy are deleted, the energy balance will show a discrepancy, and the results may be unreliable.

EXPLICIT CHECK: Track the mass and energy removed by element deletion. Large mass or energy removal can indicate excessive element deletion and may invalidate the energy balance. The deleted quantities should be reported and assessed.

Controlling Numerical Artefacts

Element deletion can introduce numerical artefacts. Sudden element removal can create stress waves that propagate through the structure — these are numerical, not physical. Deleted elements can leave behind "orphan" nodes that must be managed. Contact surfaces that lose elements may have gaps that cause contact problems. These artefacts can be controlled through damage evolution (gradual rather than sudden stiffness degradation), element erosion controls (minimum element size, deletion criteria), and mesh design (regular mesh that fails cleanly). The engineer should be aware of these artefacts and check for them in the results.

Key Takeaways

• Yield, damage initiation, damage evolution and element deletion are distinct stages
• Ductile damage depends on stress triaxiality — a single strain-to-failure is not adequate
• Composite damage involves multiple modes tracked separately
• Element deletion removes mass and energy — these must be tracked in the energy balance
• Damage models require material-specific calibration data — not generic constants