Shape-Memory Actuator: Hysteresis Loop & Stroke Decay (2D)

Actuation Cycle

Applied load (stress) 150 MPa

Max heating temperature 90°C

Cycle rate 1.0 Hz

Actuator State

Austenite 0%Martensite 100%

Wire temperature

20°C

Actuation cycles N

Recoverable stroke

100.0%

Transf. temp. drift ΔT

+0.0°C

How it works

This 2D view plots the actuator's physics directly in state space instead of animating a 3D coil: the top graph is the martensite-fraction/temperature hysteresis loop (Liang–Rogers cosine model), the bottom graph is the recoverable-stroke decay curve against cycle count.

Cooling (A→M): ξ = ½[1 − cos(π·(Ms−T)/(Ms−Mf))]
Heating (M→A): ξ = ½[1 + cos(π·(T−As)/(Af−As))]

The working point (T, ξ) traces a closed loop as the wire heats and cools — the loop's width is the transformation hysteresis, and its horizontal position marks the four transformation temperatures. A faint dashed loop shows the pristine (N=0) actuator for comparison.

ε_irr(N) = ε_irr,max·(1 − e^(−N/N0))
ΔT(N)    = ΔT_max·(1 − e^(−N/N0))     N0 ∝ 1/stress

As cycles N accumulate, the loop drifts right (ΔT) and the stroke-decay chart's curve — plotted live as cycles run — settles onto its saturating exponential floor. Both effects come from the same underlying dislocation-accumulation model as the 3D actuator sim; this page just shows the mechanism as a diagram rather than a physical coil.

Applied load — higher stress accelerates dislocation accumulation, shrinking N0 (steeper early decay in the bottom chart).
Max heating temperature — sets how far right the working point travels each cycle; must clear the (drifting) A_f line to close the loop back to ξ=0.
Cycle rate — how fast the working point sweeps the loop.
Skip +200 cycles — jumps N forward instantly so the long-run drift/decay is visible without waiting through hundreds of real loops.

Cycle counts are compressed for a browser demo; the qualitative trends — saturating stroke loss and rightward transformation-temperature drift — match published SMA actuator fatigue studies.

Current hysteresis loop Pristine (N=0) loop Working point / stroke curve