Shape Memory Alloy (SMA) Model
Shape Memory Alloy (SMA): Theoretical Foundations
What are Shape Memory Alloys?
Professor, shape memory alloys (SMAs) are materials that return to their original shape even after deformation, right?
SMA (Shape Memory Alloy) is represented by NiTi (Nitinol). It exhibits two special behaviors:
1. Superelasticity (Superelasticity) — Even under large deformation (6-8% strain), it fully recovers upon unloading. Temperature is constant.
2. Shape Memory Effect — After deformation, heating causes recovery to the original shape. Phase transformation occurs with temperature change.
Phase Transformation
SMA characteristics originate from the martensite → austenite phase transformation:
- High Temperature (Austenite) — Hard. Exhibits superelasticity.
- Low Temperature (Martensite) — Soft. Heating returns it to austenite → shape recovery.
Modeling in FEM
Abaqus's *SUPERELASTIC (Superelastic SMA model). Models stress-induced martensitic transformation.
$\varepsilon^{tr}$ is the transformation strain. Stress-induced austenite → martensite transformation.
Summary
Discovery of the Shape Memory Effect
The shape memory effect of NiTi (Nitinol) alloy was accidentally discovered in 1963 by William Buehler and Frederick Wang at the US Naval Ordnance Laboratory (NOL). The alloy name "Nitinol" is derived from the initials of Nickel Titanium Naval Ordnance Laboratory. The phase transformation between martensite (low-temperature phase) and austenite (high-temperature phase) is the physical basis for shape memory and superelasticity.
Computational Methods for Shape Memory Alloy (SMA)
FEM Settings for SMA
```
*MATERIAL, NAME=NiTi
*DEPVAR
24,
*USER MATERIAL, CONSTANTS=14
$ Auricchio model parameters
```
Or:
```
*SUPERELASTIC
sigma_SL, sigma_EL, sigma_SU, sigma_EU, epsilon_L, ...
```
So the superelastic hysteresis loop (different loading-unloading paths) is reproduced in FEM, right?
Yes. Loading causes stress-induced martensitic transformation → unloading causes reverse transformation to austenite. Hysteresis dissipates energy.
Summary
Identification Experiments for the Brinson Constitutive Law
The representative SMA constitutive law by Brinson (1993) requires 5-6 parameters: phase transformation start/finish stresses (σsAs, σfAs, σsMs, σfMs) and maximum transformation strain εL. The standard procedure is to identify transformation temperatures using DSC (Differential Scanning Calorimetry) and perform isothermal tensile tests at multiple temperatures to read transformation stresses from σ-ε curves.
Shape Memory Alloy (SMA) in Practice
SMA in Practice
Practical Checklist
Design Analysis of Intravascular Stents
In designing coronary stents (diameter 3-4mm) made of Nitinol, FEA predicts the behavior where they transform to austenite at body temperature 37°C and expand the vessel wall with a force of about 0.3-0.5N. Combining Abaqus's *SUPERELASTIC keyword (Superelastic) with the Auricchio-Taylor model has been used as computational evidence for FDA 510(k) submissions since the 2010s.