Computational Mechanics

, Volume 56, Issue 3, pp 443–461 | Cite as

Numerical modeling of shape memory alloy linear actuator

  • Jaronie Mohd Jani
  • Sunan Huang
  • Martin Leary
  • Aleksandar Subic
Original Paper


The demand for shape memory alloy (SMA) actuators in high-technology applications is increasing; however, there exist technical challenges to the commercial application of SMA actuator technologies, especially associated with actuation duration. Excessive activation duration results in actuator damage due to overheating while excessive deactivation duration is not practical for high-frequency applications. Analytical and finite difference equation models were developed in this work to predict the activation and deactivation durations and associated SMA thermomechanical behavior under variable environmental and design conditions. Relevant factors, including latent heat effect, induced stress and material property variability are accommodated. An existing constitutive model was integrated into the proposed models to generate custom SMA stress–strain curves. Strong agreement was achieved between the proposed numerical models and experimental results; confirming their applicability for predicting the behavior of SMA actuators with variable thermomechanical conditions.


Finite difference method Shape memory alloy Transient Optimization 

List of Symbols


Cross-sectional area \((\mathrm{m}^{2})\)


Surface area \((\mathrm{m}^{2})\)


Austenite transformation temperatures \((^{\circ }\mathrm{C})\)


Martensite transformation temperatures \((^{\circ }\mathrm{C})\)

\({\theta }_{T}\)

Thermoelastic tensor \((\mathrm{N}/\mathrm{m}^{2}\,\mathrm{K})\)

\(\varOmega \)

Transformation tensor \([\mathrm{N}/\mathrm{m}^{2})\)

\(\alpha \)

Thermal diffusivity \((\mathrm{m}^{2}/\mathrm{s})\)

\(\upsilon \)

Kinematic viscosity \((\mathrm{m}^{2}/\mathrm{s})\)


Heat flux \((\mathrm{W}/\mathrm{m}^{2})\)

\(\xi _{M}\)

Martensite volume fraction (–)



\(\varDelta H\)

Latent heat of phase transformation (J/kg)


Specific heat capacity (J/kg K)


Stress-influenced coefficients \((\mathrm{MPa}/^{\circ }\mathrm{C})\)


Diameter (m)


Force (N)

\(\rho _{D}\)

Density \((\mathrm{kg}/\mathrm{m}^{3})\)

\(\varepsilon ^{'}\)

Emissivity (–)

\(\sigma ^{'}\)

Stephen–Boltzman constant \((\mathrm{W}/\mathrm{m}^{2}\,\mathrm{K}^{4})\)

\(\rho _{R}\)

Resistivity (\(\Omega \)m)


Heat transfer coefficient \((\mathrm{W}/\mathrm{m}^{2}\,\mathrm{K})\)

\(\sigma \)

Stress (Pa)

\(\varepsilon \)

Strain (–)


Thermal conductivity (W/m K)


Rate of Joule heating per volume \((\mathrm{W}/\mathrm{m}^{3})\)


Current density \((\mathrm{A}/\mathrm{mm}^{2})\)


Length (m)


Temperature \((\mathrm{K},\,^{\circ }\mathrm{C})\)


Velocity (m/s)


Time (s)


Radius (m)


Electrical resistance (\(\Omega \))


Spring constant (N/m)


Volume \((\mathrm{m}^{3})\)


Young’s modulus \((\mathrm{N}/\mathrm{m}^{2})\)


Biot number (–)


Fourier number (–)


Nusselt number (–)


Prandtl number (–)


Reynolds number (–)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Jaronie Mohd Jani
    • 1
    • 2
  • Sunan Huang
    • 1
  • Martin Leary
    • 1
  • Aleksandar Subic
    • 3
  1. 1.Centre for Advanced Manufacture, School of Aerospace, Mechanical and Manufacturing EngineeringRMIT UniversityMelbourneAustralia
  2. 2.Institute of Product Design and ManufacturingUniversiti Kuala LumpurKuala LumpurMalaysia
  3. 3.Swinburne ResearchSwinburne University of Technology, HawthornVictoriaAustralia

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