Fiber pull-out vs reference models
A fiber is pulled from a unit cube of matrix through a bilinear cohesive interface. Force–displacement is compared to the three references in MatFib’s comparison script: uniform-slip upper bound, linear bond, and rigid-matrix shear-lag ODE.
Single fiber in a box Inclined fiber interface Random fibres DCB cohesive crack Cohesive zone
F = 0
EfAf u″ = bw τ(u) · u(0)=0, u(L)=upull · Fpeakuni = bw L ft
The test
Matrix fills the unit cube. A fiber of diameter d = 0.05 runs along x at (y, z) = (½, ½). Face x = 0 is fixed; the tip at x = L is driven by upull. Load transfer is a tangential cohesive traction on a cylindrical interface of measure bw = π d.
Cohesive bond
- Elastic toe up to slip a0
- Peak traction ft
- Linear softening to wc = 2 Gf / ft
- Zero traction beyond wc
What each curve is
- Uniform slip — every point slips as s = upull (upper bound)
- Linear bond — constant stiffness, closed-form sinh profile
- Shear-lag ODE — rigid matrix, same cohesive law on the line
- FEM cohesive — embedded fiber + compliant matrix (slightly softer than shear-lag)
τ(s) = ft · (wc − s)/(wc − a0) a0 ≤ s ≤ wc
τ(s) = 0 s > wc
Why the references disagree
Uniform slip puts the whole interface at tip slip — an upper bound while the law rises, and an over-prediction once softening localises near the loaded end. Shear-lag lets slip vary: a debond front marches from tip to root. Matrix compliance softens the tip reaction further — the gap between FEM and the rigid-matrix ODE. Linear bond never softens, so force keeps rising with upull.
The MATLAB driver loads a nonlinear run, re-solves linear-bond FEM on the same mesh, integrates the shear-lag ODE, and reports RMSE against the uniform and shear-lag forces. An InterfaceCracking traction–opening plot is separate: same law shape, different geometry — not a pull-out curve.