Shape Memory Alloy Self-Expanding Stent

In the tree, select .

Geometry 1

The geometry sequence for the model is available in a file. If you want to create it from scratch yourself, you can follow the instructions in the Appendix — Geometry Modeling Instructions section. Otherwise, insert the geometry sequence as follows:

In the toolbar, click and choose .

Browse to the model’s Application Libraries folder and double-click the file sma_stent_geom_sequence.mph.

In the toolbar, click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

Add functions to prescribe the outer radius and temperature.


Name	Expression	Value	Description
para	0	0	Sweep parameter
pload	0[N/m^2]	0 N/m²	Applied pressure

Definitions

Interpolation 1 (int1)

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type ro.


t	f(t)
0	Ro
1	1.4[mm]
2	1.4[mm]

Locate the section. In the table, enter the following settings:


Function	Unit
ro	m

Interpolation 2 (int2)

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type temperature.

Since the study has two distinct phases, a first one with forward transformation and a second one with reverse transformation, use a function to specify the transformation direction. This will improve the time and robustness of the computation.


t	f(t)
0	-27
1	-27
2	37

Locate the section. In the table, enter the following settings:


Function	Unit
temperature	degC

Piecewise 1 (pw1)

In the toolbar, click

and choose .

In the window for , locate the section.

Find the subsection. In the table, enter the following settings:


Start	End	Function
0	1	1
1	2	-1

Create three material nodes: one for each austenite and martensite phase, and one for common properties. For now, just add the material nodes to make them available, the data required will be filled in later.

Materials

General

In the window, under right-click and choose .

In the window for , type General in the text field.

Austenite

Right-click and choose .

In the window for , type Austenite in the text field.

Martensite

Right-click and choose .

In the window for , type Martensite in the text field.

Solid Mechanics (solid)

Shape Memory Alloy 1

In the window, under right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the T list, choose . In the associated text field, type temperature(para).

Locate the section. Find the subsection. From the list, choose .

Find the subsection. From the list, choose .

Locate the section. Select the check box.

The local computations at Gauss points during assembly are expensive for the SMA model. Using a reduced integration scheme will reduce the overall simulation time.

Locate the section. Select the check box.

Phase Transformation Direction 1

In the window, expand the node, then click .

In the window for , locate the section.

From the list, choose .

In the text field, type pw1(para).

Shape Memory Alloy 1

In the window, click .

Thermal Expansion 1

In the toolbar, click

and choose .

In the window for , locate the section.

Select Boundaries 2 and 13 only.

for .

Global Definitions

Default Model Inputs

In the window, under click .

In the window for , locate the section.

Find the subsection. In the text field, type -27[degC].

Solid Mechanics (solid)

Thermal Expansion 1

In the window, under click .

In the window for , locate the section.

Find the subsection. From the list, choose .

Symmetry 1

In the toolbar, click

and choose .

Prescribe zero displacement in the z direction on one point to avoid rigid body motion.

Prescribed Displacement 1

In the toolbar, click

and choose .

Select Point 16 only.

In the window for , locate the section.

Select the check box.

Boundary Load 1

In the toolbar, click

and choose .

Select Boundaries 14–16 only.

In the window for , locate the section.

From the list, choose .

In the p text field, type pload.

Definitions

Use point integration to make the displacement available in expressions.

Integration 1 (intop1)

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Select Point 16 only.

Solid Mechanics (solid)

Now add a global equation for the applied pressure, so that the outer radius equals the prescribed one. For that, you need to show advanced physics options.

Click the

button in the toolbar.

In the dialog box, in the tree, select the check box for the node .

Global Equations 1

In the toolbar, click

and choose .

In the window for , locate the section.


Name	f(u,ut,utt,t) (1)	Initial value (u_0) (1)	Initial value (u_t0) (1/s)	Description
pload	intop1(x)-ro(para)	0	0

Locate the section. Click

In the table, enter the following settings:


Dependent variable quantity	Unit
Custom unit	Pa

In the table, enter the following settings:


Source term quantity	Unit
Custom unit	m

Materials

General (mat1)

In the window, under click .

In the window for , locate the section.


Property	Variable	Value	Unit	Property group
Shape memory alloy reference temperature	T0	293.15[K]	K	Lagoudas model
Poisson’s ratio	nu	0.33	1	Basic
Martensite start temperature	TMs	-28[degC]	K	Lagoudas model
Martensite finish temperature	TMf	-43[degC]	K	Lagoudas model
Slope of martensite limit curve	CM	7.4e6	Pa/K	Lagoudas model
Austenite start temperature	TAs	-3[degC]	K	Lagoudas model
Austenite finish temperature	TAf	7[degC]	K	Lagoudas model
Slope of austenite limit curve	CA	7.4e6	Pa/K	Lagoudas model
Maximum transformation strain	etrmaxLagoudas	0.056	1	Lagoudas model
Calibration stress level	sigmaStar	0	N/m²	Lagoudas model
Density	rho	6500	kg/m³	Basic

Austenite (mat2)

In the window, click .

In the window for , locate the section.


Property	Variable	Value	Unit	Property group
Young’s modulus	E_A	55[GPa]	Pa	Austenite phase
Heat capacity at constant pressure	Cp_A	400	J/(kg·K)	Austenite phase
Coefficient of thermal expansion	alpha_A_iso ; alpha_Aii = alpha_A_iso, alpha_Aij = 0	22e-6	1/K	Thermal expansion, austenite phase

Martensite (mat3)

In the window, click .

In the window for , locate the section.

Select Domains 1 and 3 only.


Property	Variable	Value	Unit	Property group
Young’s modulus	E_M	46[GPa]	Pa	Martensite phase
Heat capacity at constant pressure	Cp_M	400	J/(kg·K)	Martensite phase
Coefficient of thermal expansion	alpha_M_iso ; alpha_Mii = alpha_M_iso, alpha_Mij = 0	22e-6	1/K	Thermal expansion, martensite phase

Mesh 1

Mapped 1

In the toolbar, click

and choose .

Select Boundary 13 only.

Distribution 1

Right-click and choose .

Select Edge 16 only.

In the window for , locate the section.

In the text field, type 4.

Distribution 2

In the window, right-click and choose .

Select Edge 18 only.

In the window for , locate the section.

In the text field, type 3.

Swept 1

In the toolbar, click

Distribution 1

Right-click and choose .

In the window for , locate the section.

In the text field, type 20.

Distribution 2

In the window, right-click and choose .

In the window for , locate the section.

Add maximum and average operators that will be used in postprocessing.

Select Domain 2 only.

Locate the section. From the list, choose .

In the text field, type 40.

In the text field, type 8.

Select the check box.

In the window, right-click and choose .

Definitions

Maximum 1 (maxop1)

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Select Boundary 12 only.

Average 1 (aveop1)

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Study 1

Step 1: Stationary

In the window, under click .

In the window for , locate the section.

Select the check box.

Click to expand the section. Select the check box.

In the table, click to select the cell at row number 1 and column number 2.


Parameter name	Parameter value list	Parameter unit
para (Sweep parameter)

In the dialog box, type 0 in the text field.

In the text field, type 0.05.

In the text field, type 2.

Add a predefined plot of the von Mises stress.

In the window, click .

In the window for , locate the section.

Clear the check box.

In the toolbar, click

Results

Use the mouse and zoom buttons to get similar view as Figure 4.

Add Predefined Plot

Go to the window.

In the tree, select .

Click in the window toolbar.

In the toolbar, click

Results

Stress (solid)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Volume 1

In the window, expand the node, then click .

In the window for , locate the section.

From the list, choose .

Stress (solid)

In the window, click .

In the window for , locate the section.

From the list, choose .

In the toolbar, click

Now show the results at the end of crimping.

Locate the section. From the list, choose .

In the toolbar, click

From the list, choose .

Reproduce Figure 9 to show the evolution of martensite volume fraction.

Martensite Volume Fraction

In the toolbar, click

and choose .

In the window for , type Martensite Volume Fraction in the text field.

Global 1

In the toolbar, click

In the window for , locate the section.

Martensite Volume Fraction


Expression	Unit	Description
maxop1(solid.xi_M)	1	Surface Maximum
aveop1(solid.xi_M)	1	Volume Average

In the toolbar, click

In the window, click .

In the window for , click to expand the section.

From the list, choose .

In the text area, type Martensite Volume Fraction.

Locate the section. From the list, choose .

Reproduce Figure 10 to show the increase of pressure with temperature.

Pressure vs. Temperature

In the toolbar, click

and choose .

In the window for , type Pressure vs. Temperature in the text field.

Locate the section. From the list, choose .

In the list, select the solution steps from 1 to 2.

Global 1

Right-click and choose .

In the window for , locate the section.

Create new datasets to build the entire geometry of the stent and reproduce Figure 5 to Figure 8.


Expression	Unit	Description
pload	kPa	State variable pload

Locate the section. From the list, choose .

In the text field, type temperature(para).

From the list, choose .

Select the check box. In the associated text field, type Temperature.

Pressure vs. Temperature

In the window, click .

In the window for , locate the section.

Clear the check box.

In the toolbar, click

Sector 3D 1

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type 2*Ns.

From the list, choose .

Array 3D 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the text field, type 4.

Locate the section. From the list, choose .

In the text field, type hs*1.1.

Stress, Whole Stent

In the window, right-click and choose .

In the window for , type Stress, Whole Stent in the text field.

Locate the section. From the list, choose .

In the toolbar, click

Locate the section. From the list, choose .

In the toolbar, click

Locate the section. From the list, choose .

In the toolbar, click

Transformation, Whole Stent

From the list, choose .

Right-click and choose .

In the window for , type Transformation, Whole Stent in the text field.

Volume 1

In the window, expand the node, then click .

In the window for , click in the upper-right corner of the section. From the menu, choose .

Locate the section. Click

In the dialog box, select in the tree.

Transformation, Whole Stent

In the window for , locate the section.

From the list, choose .

In the window, click .

In the toolbar, click

In the window for , locate the section.

From the list, choose .

In the toolbar, click

Create animations of the last two plots.

From the list, choose .

Stress

In the toolbar, click

and choose .

In the window for , type Stress in the text field.

Locate the section. From the list, choose .

Locate the section. In the text field, type 0.2.

Click the

button in the toolbar.

Transformation

Right-click and choose .

In the window for , type Transformation in the text field.

Locate the section. From the list, choose .

Click the

button in the toolbar.

Appendix — Geometry Modeling Instructions

From the menu, choose .

In the window, click

In the window, click

In the window, under click .

In the window for , locate the section.