Cohesive-Zone Modelling for Composite Delamination

What Is It?

Cohesive-zone modelling (CZM) is a method for predicting delamination initiation and propagation in composite structures. It represents the ply interface with special elements — cohesive elements or contact-based cohesive laws — that obey a traction-separation law. The law describes how the interface transfers load as a function of the opening and sliding displacement between the surfaces. When the tractions exceed the interface strength, damage initiates; as the separation increases, the stiffness degrades and the cohesive traction softens to zero, dissipating the fracture energy. Unlike fracture-mechanics methods that require a pre-existing crack, cohesive-zone modelling captures both initiation and propagation in a single analysis.

Why It Matters

Cohesive-zone modelling is the most widely used method for delamination prediction in composite structural analysis. It handles the full delamination process — initiation at stress concentrations, propagation along the interface, and interaction with other damage modes — within a standard nonlinear FEA framework. It does not require a pre-defined crack path or an initial crack, making it suitable for problems where the initiation location is not known in advance. For damage tolerance assessment, impact analysis and joint analysis, cohesive-zone modelling provides the capability to predict whether, where and how delamination will grow.

Cohesive-zone modelling captures both delamination initiation and propagation in a single analysis — no pre-existing crack needed. It is the most widely used method for delamination prediction in composite structures.

Interface Elements and Contact-Based Cohesive Laws

Cohesive-zone modelling is implemented in two main ways. The first uses dedicated interface elements — zero-thickness or thin elements placed between solid or shell elements at the ply interfaces. These elements carry tractions (normal and shear) that depend on the relative displacement between their top and bottom faces. The second uses a contact-based cohesive law, where the standard contact formulation between surfaces is augmented with a traction-separation law. Both approaches produce the same behaviour — the interface transfers load up to the strength, then softens to zero. The choice between them depends on the solver and the modelling preferences.

• Interface elements — zero-thickness or thin elements placed between plies at each interface
• Carry tractions (normal + shear) as a function of relative displacement (separation)
• Contact-based cohesive law — standard contact formulation augmented with traction-separation law
• Both produce the same physical behaviour — load transfer, softening, failure
• Choice depends on solver capabilities and modelling preferences

Traction-Separation Behaviour

The traction-separation law is the heart of the cohesive-zone model. It defines the relationship between the traction (force per unit area) transmitted by the interface and the separation (relative displacement) between the surfaces. The law has three phases: an initial linear elastic phase where the traction increases with separation; a damage initiation point where the traction reaches the interface strength; and a softening phase where the traction decreases as the separation increases, eventually reaching zero. The area under the traction-separation curve is the fracture energy G_c — the energy dissipated per unit area as the interface fails.

Traction-separation law (conceptual):

T = traction (force per unit area)
δ = separation (relative displacement)

Phase 1 — Linear elastic (before initiation):
  T = K × δ    (K = initial stiffness)
  T increases linearly with δ

Phase 2 — Damage initiation:
  T = T_max    (interface strength / peak traction)
  δ = δ_init   (separation at initiation)

Phase 3 — Softening (after initiation):
  T decreases as δ increases
  T → 0  as  δ → δ_fail

Area under curve = fracture energy G_c
  G_c = ∫ T dδ  (integrated from 0 to δ_fail)

The shape of the softening curve (linear,
exponential, trapezoidal) is defined by
the damage evolution law.

Damage Initiation

Damage initiation in the cohesive zone is the point at which the interface traction reaches the interface strength. Before initiation, the interface is undamaged — it transfers load elastically. At initiation, the damage variable starts to increase from zero. The initiation criterion determines when this happens. The most common criterion is the quadratic nominal stress criterion, which combines the normal traction (peel) and the shear tractions. When the combined measure reaches 1.0, damage initiates. The initiation criterion and its parameters are covered in detail in the dedicated article on cohesive-zone damage initiation.

Damage initiation occurs when the interface traction reaches the interface strength. The quadratic nominal stress criterion combines peel and shear tractions — when the combined measure reaches 1.0, damage begins. See the dedicated damage initiation article for details.

Damage Evolution

After initiation, damage evolution governs how the cohesive traction softens from the peak value to zero. The evolution law defines the shape of the softening curve — linear, exponential, or trapezoidal — and the separation at which the traction reaches zero (complete failure). The evolution is tied to the fracture energy G_c: the area under the softening curve must equal G_c, ensuring the correct amount of energy is dissipated regardless of the element size. For mixed-mode loading, the evolution law combines the Mode I, Mode II and Mode III fracture energies through a mixed-mode interaction criterion. The damage evolution is covered in detail in the dedicated article on mixed-mode cohesive damage evolution.

• Damage evolution governs the softening from peak traction to zero
• Evolution law defines the softening shape — linear, exponential, trapezoidal
• Area under the softening curve = fracture energy G_c
• For mixed mode: combines G_Ic, G_IIc, G_IIIc through an interaction criterion
• Energy-based evolution ensures mesh-objective energy dissipation

Fracture Energy Dissipation

The fracture energy G_c is the energy dissipated per unit area as the cohesive zone fails. It is the single most important parameter governing the propagation behaviour — it determines how much energy the interface can absorb before it separates completely. The fracture energy is a material property obtained from fracture tests: G_Ic from the DCB test, G_IIc from the ENF test, and mixed-mode toughness from the MMB test. The cohesive law is calibrated so that the area under the traction-separation curve equals G_c. This ensures that the model predicts the correct crack growth resistance.

The fracture energy G_c governs propagation — it is the energy dissipated per unit delamination area. Obtain G_Ic from DCB, G_IIc from ENF, mixed-mode from MMB. Calibrate the cohesive law so the area under the curve equals G_c.

Delamination Propagation

One of the key strengths of cohesive-zone modelling is that it captures delamination propagation naturally. As the load increases, the cohesive elements ahead of the crack front transfer load elastically. At the crack front, the elements have initiated damage and are softening. Behind the crack front, the elements have failed completely — the traction is zero, and the surfaces are separated. The crack advances as elements progress through the softening curve. There is no need to define a crack path or to re-mesh — the cohesive elements at the interface handle the propagation automatically. This makes cohesive-zone modelling suitable for complex delamination patterns, including multiple delaminations and branched cracks.

Cohesive-zone crack propagation:

Ahead of crack front:
  δ < δ_init  →  undamaged, elastic load transfer

At crack front (process zone):
  δ_init < δ < δ_fail  →  softening, damage 0 < d < 1
  Traction decreases from T_max towards 0

Behind crack front:
  δ > δ_fail  →  fully failed, d = 1, T = 0
  Surfaces separated — delamination has grown

Crack advances as elements progress
through the softening curve.
No re-meshing needed — propagation is
handled automatically by the cohesive law.

Cohesive-Zone Modelling vs Other Methods

Cohesive-zone modelling is one of several methods for delamination prediction. Compared to strength-based methods, it captures both initiation and propagation, not just initiation. Compared to VCCT, it does not require a pre-existing crack and captures the initiation naturally. However, cohesive-zone modelling requires finer meshes at the interface to resolve the cohesive zone, and the penalty stiffness must be carefully selected. The choice between methods depends on the problem — cohesive zones are preferred when initiation and propagation both matter; VCCT is preferred when a pre-existing crack is known and only propagation is of interest.

Modelling Considerations

Several considerations affect the quality of a cohesive-zone analysis. The mesh must be fine enough to resolve the cohesive zone — the region ahead of the crack front where the tractions are between the peak and zero. If the element is too large relative to the cohesive zone length, the propagation prediction is inaccurate. The penalty stiffness must be high enough to prevent artificial compliance but low enough to avoid numerical ill-conditioning and excessively small time steps in explicit analysis. The traction-separation law shape (linear, exponential) should be selected based on the material behaviour and available test data. The mixed-mode interaction criterion should be calibrated against mixed-mode test data.

Cohesive-zone analysis quality depends on: (1) mesh fine enough to resolve the cohesive zone, (2) penalty stiffness balanced between artificial compliance and ill-conditioning, (3) law shape selected for the material, (4) mixed-mode criterion calibrated against test data.

Cross-Links

This article is the cornerstone for the cohesive-zone modelling group. The subsequent articles cover the traction-separation law in detail, the damage initiation criteria, the mixed-mode damage evolution, the mesh requirements, the stiffness selection, and the verification of cohesive-zone models. Related content in the broader knowledge base covers delamination fundamentals, interlaminar stress, and progressive damage analysis.

• Traction-separation laws — detailed law formulation
• Cohesive-zone damage initiation — initiation criteria in detail
• Mixed-mode cohesive damage evolution — mixed-mode interaction laws
• Cohesive-zone mesh requirements — element size and cohesive zone length
• Cohesive stiffness selection — penalty stiffness and its effects
• Cohesive-zone model verification — DCB, ENF, mixed-mode verification
• Delamination fundamentals — the physics of delamination
• Interlaminar stress fundamentals — the stresses that drive delamination

Key Takeaways

• Cohesive-zone modelling captures delamination initiation and propagation in one analysis — no pre-existing crack needed
• Interface elements or contact-based cohesive laws implement the traction-separation behaviour
• Traction-separation law: linear elastic → initiation (peak traction) → softening → failure (zero traction)
• Fracture energy G_c = area under the traction-separation curve — governs propagation
• Propagation is handled automatically as elements soften and fail — no re-meshing needed
• Quality depends on mesh resolution, stiffness selection, law shape, and mixed-mode calibration