# Thermal Stress Analysis of Polymeric Photo-Thermal Microactuator

## Overview

The aim of this test case is to validate the following functions:

• thermomechanical solvers

The simulation results of SimScale were compared to the analytical results presented in [Elbuken]. The meshes used were created using second order tetrahedral automatic meshing algorithm on the SimScale platform.

Import validation project into workspace

## Geometry

The radius (R) and thickness of the microactuator was set to 130 μm and 100 μm respectively and remained constant for all the cases. For cases from A1 to A5 the length (L) and width (W) of the microactuator arm was remained constant at 1000 μm and 50 μm respectively whereas the bending angle (θ) was changed from 6° to 14°. For cases from B1 to B8 the length (L) and bending angle (θ) of the microactuator arm was remained constant at 700 μm and 6° respectively whereas the width (W) was changed from 30 μm to 100 μm. Due to symmetry, only half of the model was taken for the analysis. The skeleton of the geometry used for the analysis is shown in the figure below:

## Analysis type and Domain

Tool Type : CalculiX, Code_Aster

Analysis Type : Thermomechanical

Mesh and Element types :

Information of all tested cases
Case Arm length (μm) Width (μm) Bending angle (°) Mesh algorithm No. of nodes No. of 3D elements Solver
A1-1/2 1000 50 6 Tetrahedral automatic 23652 14408 CalculiX/Code_Aster
A2-1/2 1000 50 8 Tetrahedral automatic 23147 14046 CalculiX/Code_Aster
A3-1/2 1000 50 10 Tetrahedral automatic 23713 14330 CalculiX/Code_Aster
A4-1/2 1000 50 12 Tetrahedral automatic 22525 13586 CalculiX/Code_Aster
A5-1/2 1000 50 14 Tetrahedral automatic 22724 13670 CalculiX/Code_Aster
B1-1/2 700 30 6 Tetrahedral automatic 29407 18758 CalculiX/Code_Aster
B2-1/2 700 40 6 Tetrahedral automatic 31521 20498 CalculiX/Code_Aster
B3-1/2 700 50 6 Tetrahedral automatic 30997 20243 CalculiX/Code_Aster
B4-1/2 700 60 6 Tetrahedral automatic 33551 22158 CalculiX/Code_Aster
B5-1/2 700 70 6 Tetrahedral automatic 26071 16664 CalculiX/Code_Aster
B6-1/2 700 80 6 Tetrahedral automatic 28881 18754 CalculiX/Code_Aster
B7-1/2 700 90 6 Tetrahedral automatic 21715 13479 CalculiX/Code_Aster
B8-1/2 700 100 6 Tetrahedral automatic 22347 22347 CalculiX/Code_Aster

Mesh used for case A1 and B1 are shown in the figures below.

## Simulation Setup

Material:

• SU-8: isotropic: E
$E$

= 4 GPa, μ

$\mu$

= 0.22, ρ

$\rho$

= 1200 kg/m³, κ

$\kappa$

= 0.2 W/(mK), Expansion coefficient = 52 e-6 1/K, Reference temperature = 300 K, Specific heat = 1500 J/(kg K)

Initial Condition:

• Temperature = 300 K

Constraints:

• Face ABCD constrained in all directions
• Face IJKL constrained in x-direction only

Temperature Loads:

• Constant temperature of 300 K on face ABCD

Heat Flux Loads:

• Laser surface heat flux of 9433.96 W/m² (0.5 mW) on face IGMOK
• Convective heat flux with h
$h$

= 10 W/(m²K) and Reference temperature = 300 K on faces AEIKOMGC, GHMN, MNPO, KLOP, CGHD, BFJLPNHD, AEFB, EIJF

## Results

Comparison of the tip deflection dependence on bending angle and arm width from SimScale with [Elbuken].

## References

 [Elbuken] (1, 2, 3) Elbuken, Caglar, et al. “Design and analysis of a polymeric photo-thermal microactuator.” Sensors and Actuators A: Physical 147.1 (2008): 292-299.