Each pair of neighboring atoms interacts through a Lennard-Jones pair potential U(r) = 4ε[(σ/r)¹² − (σ/r)⁶], where ε sets how deep the energy well is (bond strength) and σ sets the length scale (the atoms rest at r₀ = 2^(1/6)σ). The lattice is quasi-statically stretched along x by the strain slider; every bond's restoring force F(r) = 24ε/r·[2(σ/r)¹² − (σ/r)⁶] is summed across the sample's mid-cross-section and divided by its area to get the macroscopic stress plotted below.
U(r) = 4ε[(σ/r)¹² − (σ/r)⁶]
F(r) = 24ε/r·[2(σ/r)¹² − (σ/r)⁶]
stress = Σ F_x(bonds crossing mid-plane) / area
- ε (well depth) — deeper wells mean stronger bonds: the stress-strain slope (elastic modulus) and the peak stress both scale up directly with ε.
- σ (spacing) — sets the equilibrium bond length; changing it rebuilds the lattice at a new scale.
- Structure — Simple Cubic gives each atom 6 nearest neighbours; Close-Packed (FCC) gives 12, roughly doubling stiffness for the same ε/σ.
- Fracture — a bond snaps once it is stretched past the potential's inflection radius r* = (26/7)^(1/6)σ, where the restoring force peaks and then softens — the atoms drift apart and the curve turns over, just like a real tensile test past its ultimate strength.
- Save as Compare — freezes the current curve as a dashed reference (B) so you can change ε, σ or structure and see curve A move relative to it.