What does this equation mean?

The mechanical-metamaterials case sharpens the same point from a different angle. A computationally designed lattice — an octet truss or similar architected structure — can be optimized in silico for a target stiffness-to-weight ratio, and DFT-adjacent atomistic methods can predict the base material’s elastic constants reasonably well. Whether the as-manufactured lattice reaches that target depends on print-defect statistics, strut-level stress concentration, and fatigue behavior under cyclic loading that only a physical tensile or fatigue rig captures, because those failure modes emerge from manufacturing variance and load history, not from the unit cell’s idealized geometry. This Palmgren–Miner-style cumulative-damage sum, where $n_i$ is cycles actually applied at a given stress level and $N_i$ is the cycles-to-failure at that same stress level, is a first-order engineering approximation, not a fundamental law — it assumes damage accumulates linearly and independently of load sequence, an assumption known to break down under highly variable loading. It is included here specifically because it exposes that assumption rather than to dress up the argument in notation: fatigue life is a property of load history applied to a real manufactured part, and no discovery-stage calculation, however accurate about the pristine lattice, substitutes for measuring it.