{"id":18481,"date":"2018-12-19T11:38:03","date_gmt":"2018-12-19T11:38:03","guid":{"rendered":"https:\/\/www.simscale.com\/?page_id=18481"},"modified":"2026-02-08T00:33:09","modified_gmt":"2026-02-08T00:33:09","slug":"thermal-stress-analysis-of-polymeric-photo-thermal-microactuator","status":"publish","type":"page","link":"https:\/\/www.simscale.com\/docs\/validation-cases\/thermal-stress-analysis-of-polymeric-photo-thermal-microactuator\/","title":{"rendered":"Validation Case: Thermal Stress Analysis of Polymeric Photo-Thermal Microactuator"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">This thermal stress analysis of a polymeric photo-thermal microactuator validation case belongs to thermomechanics. This test case aims to validate the following:<\/p>\n\n\n\n\n\n\n<ul class=\"wp-block-list\">\n<li>Thermomechanical solvers<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The simulation results of SimScale were compared to the analytical results presented in [Elbuken <em>et al.<\/em>]\\(^1\\).<\/p>\n\n\n\n<div class=\"hw-block hw-btnWrapper hw-btnWrapper--alignCenter \">\n    <a href=\"https:\/\/www.simscale.com\/workbench\/?pid=210554508567397953\" class=\"hw-btn    \" rel=\"noopener \" target=\"_blank\"    >\n        View Project    <\/a>\n<\/div>\n\n\n\n\n<h2 id=\"geometry\" class=\"wp-block-heading\" >Geometry<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A total of 13 microactuator geometries are evaluated in this validation case. The base geometry is shown below:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-19_12-43-07.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"947\" height=\"459\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-19_12-43-07.jpg\" alt=\"microactuator for thermal stress analysis validation\" class=\"wp-image-31575\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-19_12-43-07.jpg 947w, https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-19_12-43-07-300x145.jpg 300w, https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-19_12-43-07-768x372.jpg 768w\" sizes=\"auto, (max-width: 947px) 100vw, 947px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 1: Representation of the microactuator geometries used in the present validation project.<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">The 13 geometries are divided into two groups. Using Figure 2 as a reference, for the group A geometries, the length <em>L<\/em> and width <em>W<\/em> of the microactuator remains constant, whereas the bending angle \\(\\theta\\) varies.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For group B, the length <em>L<\/em> and bending angle \\(\\theta\\) are constant, and the width <em>W<\/em> changes. For all geometries, the radius <em>R<\/em> and thickness of the microactuator, in the y-direction, remains constant. Due to symmetry, only half of the model was taken for the analysis.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/microactuator-angles.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"393\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/microactuator-angles-1024x393.jpg\" alt=\"schematic of the geometries used in the project\" class=\"wp-image-31377\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/microactuator-angles-1024x393.jpg 1024w, https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/microactuator-angles-300x115.jpg 300w, https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/microactuator-angles-768x294.jpg 768w, https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/microactuator-angles.jpg 1244w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 2: Schematic of the geometries used in the present validation case.<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Table 1 provides an overview of the dimensions:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>Case<\/strong><\/td><td><strong>R \\([\\mu m]\\)<\/strong><\/td><td><strong>Thickness in y-direction <strong><strong><strong>\\([\\mu m]\\)<\/strong><\/strong><\/strong><\/strong><\/td><td><strong>W <strong><strong><strong>\\([\\mu m]\\)<\/strong><\/strong><\/strong><\/strong><\/td><td><b>L <\/b>\\([\\mu m]\\)<\/td><td><strong>\\(\\theta\\) [\u00ba]<\/strong><\/td><\/tr><tr><td>A1<\/td><td>130<\/td><td>100<\/td><td>50<\/td><td>1000<\/td><td>6<\/td><\/tr><tr><td>A2<\/td><td>130<\/td><td>100<\/td><td>50<\/td><td>1000<\/td><td>8<\/td><\/tr><tr><td>A3<\/td><td>130<\/td><td>100<\/td><td>50<\/td><td>1000<\/td><td>10<\/td><\/tr><tr><td>A4<\/td><td>130<\/td><td>100<\/td><td>50<\/td><td>1000<\/td><td>12<\/td><\/tr><tr><td>A5<\/td><td>130<\/td><td>100<\/td><td>50<\/td><td>1000<\/td><td>14<\/td><\/tr><tr><td>B1<\/td><td>130<\/td><td>100<\/td><td>30<\/td><td>700<\/td><td>6<\/td><\/tr><tr><td>B2<\/td><td>130<\/td><td>100<\/td><td>40<\/td><td>700<\/td><td>6<\/td><\/tr><tr><td>B3<\/td><td>130<\/td><td>100<\/td><td>50<\/td><td>700<\/td><td>6<\/td><\/tr><tr><td>B4<\/td><td>130<\/td><td>100<\/td><td>60<\/td><td>700<\/td><td>6<\/td><\/tr><tr><td>B5<\/td><td>130<\/td><td>100<\/td><td>70<\/td><td>700<\/td><td>6<\/td><\/tr><tr><td>B6<\/td><td>130<\/td><td>100<\/td><td>80<\/td><td>700<\/td><td>6<\/td><\/tr><tr><td>B7<\/td><td>130<\/td><td>100<\/td><td>90<\/td><td>700<\/td><td>6<\/td><\/tr><tr><td>B8<\/td><td>130<\/td><td>100<\/td><td>100<\/td><td>700<\/td><td>6<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Table 1: Microactuator dimensions for the various cases.<\/figcaption><\/figure>\n\n\n\n<h2 id=\"analysis-type-and-mesh\" class=\"wp-block-heading\" >Analysis Type and Mesh<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Tool Type<\/strong>: <a href=\"https:\/\/code-aster.org\/V2\/\">Code Aster<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Analysis Type<\/strong>: <a href=\"https:\/\/www.simscale.com\/docs\/analysis-types\/thermomechanical\/\">Thermomechanical analysis type<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Mesh and Element Types<\/strong>: All meshes were created with the <a href=\"https:\/\/www.simscale.com\/docs\/simulation-setup\/meshing\/standard\/\">standard algorithm<\/a>, using second-order elements. Table 2 presents a summary of the meshes:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>Case<\/strong><\/td><td><strong>Mesh Type<\/strong><\/td><td><strong>Nodes<\/strong><\/td><td><strong>Element Type<\/strong><\/td><\/tr><tr><td>A1<\/td><td>2nd-order standard<\/td><td>194853<\/td><td>Standard<\/td><\/tr><tr><td>A2<\/td><td>2nd-order standard<\/td><td>479747<\/td><td>Standard<\/td><\/tr><tr><td>A3<\/td><td>2nd-order standard<\/td><td>360734<\/td><td>Standard<\/td><\/tr><tr><td>A4<\/td><td>2nd-order standard<\/td><td>466753<\/td><td>Standard<\/td><\/tr><tr><td>A5<\/td><td>2nd-order standard<\/td><td>257295<\/td><td>Standard<\/td><\/tr><tr><td>B1<\/td><td>2nd-order standard<\/td><td>102941<\/td><td>Standard<\/td><\/tr><tr><td>B2<\/td><td>2nd-order standard<\/td><td>134074<\/td><td>Standard<\/td><\/tr><tr><td>B3<\/td><td>2nd-order standard<\/td><td>130987<\/td><td>Standard<\/td><\/tr><tr><td>B4<\/td><td>2nd-order standard<\/td><td>132192<\/td><td>Standard<\/td><\/tr><tr><td>B5<\/td><td>2nd-order standard<\/td><td>142016<\/td><td>Standard<\/td><\/tr><tr><td>B6<\/td><td>2nd-order standard<\/td><td>152533<\/td><td>Standard<\/td><\/tr><tr><td>B7<\/td><td>2nd-order standard<\/td><td>165596<\/td><td>Standard<\/td><\/tr><tr><td>B8<\/td><td>2nd-order standard<\/td><td>173364<\/td><td>Standard<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Table 2: Overview of the mesh, creep formulation, and element technology used for each case.<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Find below the mesh used for case B8. It&#8217;s a standard mesh with second-order tetrahedral cells.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/microactuator-mesh.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"774\" height=\"536\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/microactuator-mesh.jpg\" alt=\"second order standard mesh\" class=\"wp-image-31430\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/microactuator-mesh.jpg 774w, https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/microactuator-mesh-300x208.jpg 300w, https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/microactuator-mesh-768x532.jpg 768w\" sizes=\"auto, (max-width: 774px) 100vw, 774px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 3: Second-order standard mesh used for case B8.<\/figcaption><\/figure>\n<\/div>\n\n\n<h2 id=\"simulation-setup\" class=\"wp-block-heading\" >Simulation Setup<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Material<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Custom material &#8211; SU-8<ul><li><em>Material behavior<\/em>: <em>linear elastic<\/em><\/li><\/ul>\n<ul class=\"wp-block-list\">\n<li>\\(E\\) = 4 \\(GPa\\)<\/li>\n\n\n\n<li>\\(\\nu\\) = 0.22<\/li>\n\n\n\n<li>\\(\\rho\\) = 1200 \\(kg\/m\u00b3\\)<\/li>\n\n\n\n<li>\\(\\kappa\\) = 0.2 \\(\\frac {W}{m.K}\\)<\/li>\n\n\n\n<li><em>Expansion coefficient<\/em> = 5.2e-5 \\(1\/K\\)<\/li>\n\n\n\n<li>\\(T_0\\) <em>Reference temperature<\/em> = 300 \\(K\\)<\/li>\n\n\n\n<li><em>Specific heat<\/em> = 1500 \\(\\frac {J}{kg.K}\\)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Boundary Conditions<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Constraints\n<ul class=\"wp-block-list\">\n<li>Fixed support on face ABCD;<\/li>\n\n\n\n<li>\\(d_x\\) = 0 on face JIQKL.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Temperature loads\n<ul class=\"wp-block-list\">\n<li><em>Fixed temperature value<\/em> of 300 \\(K\\) on face ABCD.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>Heat flux loads\n<ul class=\"wp-block-list\">\n<li><em>Surface heat flux<\/em> boundary condition of 9433.96 \\(W\/m\u00b2\\) face IEGMQ. <\/li>\n\n\n\n<li><em>Convective heat flux<\/em> boundary condition on all faces, except ABCD and JIQKL. The <em>heat transfer coefficient<\/em> is 10 \\(\\frac {W}{K.m^2}\\) and the \\(T_0\\) <em>reference temperature<\/em> is 300 \\(K\\).<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h2 id=\"reference-solution\" class=\"wp-block-heading\" >Reference Solution<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The analytical solution is given by the equations presented in [Elbuken <em>et al.<\/em>]\\(^1\\).<\/p>\n\n\n\n<h2 id=\"result-comparison\" class=\"wp-block-heading\" >Result Comparison<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">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).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The first plot shows the results for cases A1 through A5:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-14_18-58-44-1.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"603\" height=\"419\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-14_18-58-44-1.jpg\" alt=\"validation case results microactuator thermomechanical\" class=\"wp-image-31447\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-14_18-58-44-1.jpg 603w, https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-14_18-58-44-1-300x208.jpg 300w\" sizes=\"auto, (max-width: 603px) 100vw, 603px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 4: Comparing SimScale case A results with the analytical solution from [Elbuken]\u00b9.<\/figcaption><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Similarly, for cases B1 through B8, Figure 5 shows the result comparison:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-14_18-59-09.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"603\" height=\"419\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-14_18-59-09.jpg\" alt=\"validation case b results microactuator thermomechanical\" class=\"wp-image-31448\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-14_18-59-09.jpg 603w, https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-14_18-59-09-300x208.jpg 300w\" sizes=\"auto, (max-width: 603px) 100vw, 603px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 5: Comparing SimScale case B results with the analytical solution from [Elbuken]\u00b9.<\/figcaption><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">In Figure 6, we can see the displacement contours for case B8:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><a href=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-14_19-13-04.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"757\" height=\"614\" src=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-14_19-13-04.jpg\" alt=\"displacement contours thermomechanical validation\" class=\"wp-image-31449\" srcset=\"https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-14_19-13-04.jpg 757w, https:\/\/frontend-assets.simscale.com\/media\/2020\/07\/2020-07-14_19-13-04-300x243.jpg 300w\" sizes=\"auto, (max-width: 757px) 100vw, 757px\" \/><\/a><figcaption class=\"wp-element-caption\">Figure 6: Displacement contours for case B8.<\/figcaption><\/figure>\n<\/div>\n\n\n\n<div class='hw-block hw-references hw-references'>\n    <p class='hw-references__title'>References<\/p>\n    <ul class='hw-references__list'>\n\n        <li><cite><a href=\"https:\/\/www.sciencedirect.com\/science\/article\/abs\/pii\/S0924424708002501\" target=\"_blank\">\u201cCaglar Elbuken, Lin Gui, Carolyn L. Ren, Mustafa Yavuz, Mir Behrad Khamesee,\r\nDesign and analysis of a polymeric photo-thermal microactuator,\r\nSensors and Actuators A: Physical,\r\nVolume 147, Issue 1,\r\n2008,\r\nPages 292-299.&#8221;<\/a><\/cite><\/li>\n    <\/ul>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>This thermal stress analysis of a polymeric photo-thermal microactuator validation case belongs to thermomechanics. This...","protected":false},"author":94,"featured_media":31449,"parent":17191,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"templates\/template-documentation.php","meta":{"_acf_changed":false,"_crdt_document":"","inline_featured_image":false,"footnotes":""},"class_list":["post-18481","page","type-page","status-publish","has-post-thumbnail","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages\/18481","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/users\/94"}],"replies":[{"embeddable":true,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/comments?post=18481"}],"version-history":[{"count":0,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages\/18481\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/pages\/17191"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/media\/31449"}],"wp:attachment":[{"href":"https:\/\/www.simscale.com\/wp-json\/wp\/v2\/media?parent=18481"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}