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Single fiber in a box under tension

A unit cube of matrix is stretched in x. One fiber sits entirely inside the box — it does not reach the faces and is not pulled at a tip. Load enters through the matrix; the cohesive interface then loads the fiber. Right-face ux is taken to 0.5, the MatFib ramp that drives slip past the tail along almost the whole fiber. The force plot is the extra left-face reaction relative to matrix-only.

Fiber pull-out Inclined fiber interface Random fibres

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Rising branch
ux = 0
Rx = 0

EfAf uf″ = bw τ(uf − εx) · uf′(tips) = 0 · left face fixed, right ux → 0.5 (full debond)

Not a pull-out test

Pull-out drives the fiber tip while the matrix is held. Here the opposite happens, matching MatFib’s FinalProgram_full_1F_NonlinearInterface: the matrix cube is loaded, and the fiber is an interior inclusion. Endpoints are (0.21, ½, ½) → (0.81, ½, ½). Face x = 0 is fully fixed; face x = 1 has prescribed ux → 0.5 with uy, uz free.

Discretization (MATLAB)

  • Unit cube, structured H8 matrix
  • Fiber as 3-D truss bars, 20 segments
  • Newton–Cotes interface along the fiber
  • Em = 1, ν = 0, Ef = 104, d = 0.01

What you are watching

  • Matrix only — cube stiffness with no fiber
  • Linear bond — constant kt = 100, Cox shear-lag
  • Cohesive — same 1-D fiber, nonlinear τ(s)
  • At ux = 0.5 the fiber is unloaded: ΔRx → 0, rings grey
smooth: τ(s) = A s exp(−B s²)   A = e ft²/Gf  B = (ft/Gf)² e/2
v2: τ = ft s/a0 (toe), then linear softening to wc = 2 Gf/ft

Why the tips go first

Far-field matrix motion is um = ε x with ε = ux/L. The fiber is orders of magnitude stiffer, so its strain is smaller and more uniform. Relative slip s = uf − um therefore peaks at the ends (Cox shear-lag). Traction-free tips force N = 0 there; axial force builds toward the mid-fiber. Once |s| passes the peak of the bond law, softening fronts march inward from both tips — the same progressive debonding the MATLAB NR solve records on the 3-D mesh.

This page solves that 1-D embedded-fiber problem live (bars + nodal Newton–Cotes bond, displacement-controlled NR), which is the reduced model of the 3-D H8 + bar assembly. Matrix compliance around the fiber is omitted, so the cohesive curve is a slightly stiffer cousin of the MATLAB RVE reaction. The MATLAB run at ux = 0.5 reports 34/40 Gauss points in the tail and Rx equal to the matrix-only value; only a vanishing core at mid-fiber still sits below the tail threshold (slip is kinematically zero there). After that, ΔRx is gone and the cube behaves as matrix-only.