A shape-memory polymer (SMP) network has fixed net-points that remember one permanent (straight) shape, and flexible switching segments whose mobility freezes below the glass-transition temperature Tg. Programming deforms the strip above Tg, then cools it under strain so the switching segments vitrify and lock the temporary bent shape in place.
This 2D engine ties the strip's live curvature directly to the same sigmoid that governs the storage modulus, so the frozen-shape fraction and the modulus fraction share one glass transition by construction:
E(T) = E_r + (E_g − E_r) / (1 + exp((T − Tg)/w))
S(T) = (E(T) − E_r) / (E_g − E_r) // frozen-shape fraction, 1..0
angle(T) = programmedAngle · S(T)
Rr(T) = 1 − S(T) // recovery ratio
Below Tg (S≈1) the strip stays fully in its programmed bend regardless of how it got there — vitrified segments have no mobility to relax. Once the chamber temperature climbs past Tg (S falls toward 0) the net-points' stored entropic elasticity pulls the strip back toward its straight memory shape, and the modulus collapses across the very same transition — watch the two live curves on the right cross their half-height exactly at the same Tg mark.
- Chamber temperature — the target temperature the actuator is driven toward.
- Heating rate — how fast the actual temperature ramps toward that target (thermal lag).
- Programmed bend angle — total curvature locked in the temporary shape.
- Material — sets Tg and the transition width w, which controls whether recovery snaps sharply or unrolls gradually.
Real-world relevance: this is the same working principle behind SMP self-deploying stents, foldable space structures, and thermally triggered soft-robotic grippers.