The companion 3D simulator shows how load transfers along the length of one isolated nanofiller via interfacial shear (the Cox/Kelly–Tyson model). Real composites are full of fillers packed side by side — when one locally debonds or cracks, its load doesn't vanish, it gets handed off to its neighbors through the matrix. That lateral hand-off is a different shear-lag problem (in the tradition of Hedgepeth's discrete fiber-array model), and it is what this 2D view solves exactly:
d²Nᵢ/dx² = K·(2Nᵢ − Nᵢ₋₁ − Nᵢ₊₁) (Nᵢ(x) = axial load on filler i, x along its length)
at x=0: defect filler sheds load, split equally onto its nearest "spread" neighbors
Nᵢ(x) → N₀ = Ef·ε as x → ±∞ (far-field, undisturbed stress)
This is solved exactly by diagonalizing the array's coupling matrix (its graph Laplacian) into independent decay modes e−ωₘ|x|, then projecting the self-equilibrated load hand-off onto those modes — no iteration, no approximation. The heatmap shows Nᵢ(x)/N₀ across every filler (rows) and position (columns): the defect filler dips blue near x=0 and recovers toward the baseline color moving outward, while its neighbors flash amber/red — carrying more than the far-field stress — right at the crack plane, then relax back once the shear has redistributed the load smoothly.
- Fillers in array N — how many parallel nanofillers sit side-by-side in this cross-section; wider arrays let the concentration spread further before the group boundary matters.
- Matrix shear coupling K — how stiffly the matrix ties neighboring fillers together; higher K sharpens the stress-transfer zone into a shorter recovery length.
- Defect severity — how completely the debonded filler loses its share of load right at the crack plane (100% = fully unloaded there, matching a clean break).
- Load-sharing spread — how many neighbors on each side absorb the shed load; spreading it over more fillers lowers the peak concentration on any single one, exactly the protective effect a well-dispersed (vs. clumped) filler network provides.
- Applied strain ε — sets the undisturbed far-field stress N₀ = Eꜰ·ε used to convert the dimensionless field into real GPa/MPa readouts.
This is the mechanism behind why dispersion quality matters as much as loading fraction in real nanocomposites: a poorly dispersed filler network concentrates load onto isolated neighbors when one filler fails locally, while a well-dispersed one spreads that load thin enough that damage doesn't cascade.