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    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:

    microactuator for thermal stress analysis validation
    Figure 1: Representation of the microactuator geometries used in the present validation project.

    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.

    schematic of the geometries used in the project
    Figure 2: Schematic of the geometries used in the present validation case.

    Table 1 provides an overview of the dimensions:

    CaseR \([\mu m]\)Thickness in y-direction \([\mu m]\)W \([\mu m]\)L \([\mu m]\)\(\theta\) [º]
    Table 1: Microactuator dimensions for the various cases.

    Analysis Type and Mesh

    Tool Type: Code Aster

    Analysis Type: Thermomechanical analysis type

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

    CaseMesh TypeNodesElement Type
    A12nd-order standard194853Standard
    A22nd-order standard479747Standard
    A32nd-order standard360734Standard
    A42nd-order standard466753Standard
    A52nd-order standard257295Standard
    B12nd-order standard102941Standard
    B22nd-order standard134074Standard
    B32nd-order standard130987Standard
    B42nd-order standard132192Standard
    B52nd-order standard142016Standard
    B62nd-order standard152533Standard
    B72nd-order standard165596Standard
    B82nd-order standard173364Standard
    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.

    second order standard mesh
    Figure 3: Second-order standard mesh used for case B8.

    Simulation Setup


    • 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:

    validation case results microactuator thermomechanical
    Figure 4: Comparing SimScale case A results with the analytical solution from [Elbuken]¹.

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

    validation case b results microactuator thermomechanical
    Figure 5: Comparing SimScale case B results with the analytical solution from [Elbuken]¹.

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

    displacement contours thermomechanical validation
    Figure 6: Displacement contours for case B8.

    Last updated: November 7th, 2023