Validation Case: Thermal Stress Analysis of Polymeric Photo-Thermal Microactuator

This thermal stress analysis of a polymeric photo-thermal microactuator validation case belongs to thermomechanics. This test case aims to validate the following:

Thermomechanical solvers

The simulation results of SimScale were compared to the analytical results presented in [Elbuken et al.]\(^1\).

A total of 13 microactuator geometries are evaluated in this validation case. The base geometry is shown below:

The 13 geometries are divided into two groups. Using Figure 2 as a reference, for the group A geometries, the length L and width W of the microactuator remains constant, whereas the bending angle \(\theta\) varies.

For group B, the length L and bending angle \(\theta\) are constant, and the width W changes. For all geometries, the radius R and thickness of the microactuator, in the y-direction, remains constant. Due to symmetry, only half of the model was taken for the analysis.

Table 1 provides an overview of the dimensions:

Case

R \([\mu m]\)

Thickness in y-direction \([\mu m]\)

W \([\mu m]\)

L \([\mu m]\)

\(\theta\) [º]

A1

130

100

50

1000

6

A2

130

100

50

1000

8

A3

130

100

50

1000

10

A4

130

100

50

1000

12

A5

130

100

50

1000

14

B1

130

100

30

700

6

B2

130

100

40

700

6

B3

130

100

50

700

6

B4

130

100

60

700

6

B5

130

100

70

700

6

B6

130

100

80

700

6

B7

130

100

90

700

6

B8

130

100

100

700

6

Table 1: Microactuator dimensions for the various cases.

Mesh and Element Types: All meshes were created with the standard algorithm, using second-order elements. Table 2 presents a summary of the meshes:

Case

Mesh Type

Nodes

Element Type

A1

2nd-order standard

194853

Standard

A2

2nd-order standard

479747

Standard

A3

2nd-order standard

360734

Standard

A4

2nd-order standard

466753

Standard

A5

2nd-order standard

257295

Standard

B1

2nd-order standard

102941

Standard

B2

2nd-order standard

134074

Standard

B3

2nd-order standard

130987

Standard

B4

2nd-order standard

132192

Standard

B5

2nd-order standard

142016

Standard

B6

2nd-order standard

152533

Standard

B7

2nd-order standard

165596

Standard

B8

2nd-order standard

173364

Standard

Table 2: Overview of the mesh, creep formulation, and element technology used for each case.

Find below the mesh used for case B8. It’s a standard mesh with second-order tetrahedral cells.

Simulation Setup

Material:

Custom material – SU-8

Material behavior: linear elastic

\(E\) = 4 \(GPa\)

\(\nu\) = 0.22

\(\rho\) = 1200 \(kg/m³\)

\(\kappa\) = 0.2 \(\frac {W}{m.K}\)

Expansion coefficient = 5.2e-5 \(1/K\)

\(T_0\) Reference temperature = 300 \(K\)

Specific heat = 1500 \(\frac {J}{kg.K}\)

Boundary Conditions:

Constraints

Fixed support on face ABCD;

\(d_x\) = 0 on face JIQKL.

Temperature loads

Fixed temperature value of 300 \(K\) on face ABCD.

Heat flux loads

Surface heat flux boundary condition of 9433.96 \(W/m²\) face IEGMQ.

Convective heat flux boundary condition on all faces, except ABCD and JIQKL. The heat transfer coefficient is 10 \(\frac {W}{K.m^2}\) and the \(T_0\) reference temperature is 300 \(K\).

Reference Solution

The analytical solution is given by the equations presented in [Elbuken et al.]\(^1\).

Result Comparison

Find below the comparison between the analytical solution and SimScale results. The quantity measured is the displacement of the tip of the structure (face OPLK).

The first plot shows the results for cases A1 through A5:

Similarly, for cases B1 through B8, Figure 5 shows the result comparison:

In Figure 6, we can see the displacement contours for case B8:

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