The flagship 3D version assumes the bondline ahead of the crack tip is perfectly rigid until it fails outright, then solves a closed-form quartic for the crack length that keeps the beam-theory energy release rate exactly at GIc. This 2D model makes no such assumption: it discretizes the bondline into ~40 stations and gives each one a real bilinear traction–separation law (a cohesive zone model, the same family of model used in finite-element fracture codes):
t(δ) = k₀·δ 0 ≤ δ ≤ δ₀ (elastic)
t(δ) = t_max·(δ_f−δ)/(δ_f−δ₀) δ₀ < δ ≤ δ_f (softening)
t(δ) = 0 δ > δ_f (failed)
area under the curve = ½·t_max·δ_f = G_Ic (calibrated per ply system)
Each frame, the beam's governing equation EI·w⁽⁽⁽⁽ + κ(x)·w = 0 is assembled as an exact linear system (not an iterative relaxation) over the discretized stations, with κ(x) set by each station's own damage history, and solved directly. The grip load P is then recovered as the exact energy-conjugate reaction to the prescribed opening (a discrete Castigliano derivative), which this model's own numbers confirm matches the classic single-cantilever formula P=3EIδ/2a³ to within a few percent while the interface is still fully bonded — and reads systematically lower once loading starts, because a finite-stiffness interface is measurably more compliant than an idealized rigid bond.
The crack length a is not solved for — it emerges as the point where local damage reaches 1 (fully failed). Because real bondlines have a finite process zone (a band of partially-damaged material ahead of the traceable crack tip, typically millimeters wide for these ply systems), this model's own a(δ) reads visibly shorter than the idealized rigid-bond quartic used in the 3D version for the same opening — a real, well-documented effect, not a bug: process-zone compliance is exactly why measured DCB compliance calibrations differ from pure LEFM in practice.
- Fully-open length a — distance from the loaded end to the last station whose bondline has completely failed (traction ≈ 0).
- Process-zone width — how much bondline is currently partway through softening (0<damage<1); this band moves with the crack front and has zero width in a purely rigid-bond (LEFM) idealization.
- Fracture energy dissipated — running integral of the interface's own consumed fracture energy during this test (excludes the pre-existing a₀ flaw); it tracks G_Ic×(new crack area) essentially exactly, confirming the cohesive law is correctly calibrated.
- Because each station's bond fails somewhat abruptly once its neighbor lets go, real delamination growth in a stiff, brittle interface is often unstable — a fast, audible crack "pop" rather than smooth advance, which is exactly the saw-toothed load trace real ASTM D5528 tests record and this 2D model reproduces from first principles rather than by construction.
Real-world relevance: interlaminar toughness measured this way is what keeps a wing spar, wind-turbine blade or pressure-vessel wall from peeling apart ply-by-ply in service — the same physical question as the 3D version, answered with a genuinely different (and, in the un-cracked limit, independently cross-checked) numerical method.