Conjugate Mises transformation strain for six Pareto-optimal designs: (a) wave — high stress, (b) machined — high stress, (c) machined — high strain, (d) wave — mid-strain, (e) coil — high strain (half-symmetry cut), and (f) Belleville — high strain.
Shape memory alloy spring actuators convert limited material-level transformation strains into large structural displacements, yet a systematic comparison of different spring geometries under identical loading conditions has been absent in the literature. This project addresses that gap by developing a multi-objective optimization framework that evaluates four distinct spring actuator geometries—wave, machined, coil, and Belleville springs—under constant-force compressive loading with prescribed thermal actuation. All geometries share a common outer radius constraint (10 mm) to enable direct performance comparison. Each design is analyzed through finite element simulations using an explicit thermo-mechanical constitutive model (VUMAT) in ABAQUS/Explicit, and the NSGA-II algorithm identifies Pareto-optimal designs that maximize both equivalent footprint stress and actuation strain.
Pareto-optimal designs in equivalent footprint stress–actuation strain space under 300 MPa material stress. Dashed curves are iso-work lines. Circled points correspond to the visualized designs below. Literature data shown for context.
Results reveal distinct performance envelopes for each geometry: Belleville springs achieve the highest footprint-normalized work density (1.62 mJ/mm³), making them ideal for compact high-force applications. Coil springs deliver the largest actuation strains (up to 0.84) through their torsion-dominated deformation mode. Wave springs offer exceptional tunability across a wide stress–strain range. Machined springs provide superior design flexibility, spanning more than one order of magnitude in equivalent footprint stress through their five-parameter design space.
Graduate Student: Sefa Oksuz