{"id":1230,"date":"2022-01-26T10:40:02","date_gmt":"2022-01-26T15:40:02","guid":{"rendered":"https:\/\/research.gsd.harvard.edu\/maps\/2022\/01\/26\/inclined-auxetic-metamaterials-buckling\/"},"modified":"2025-02-21T13:16:37","modified_gmt":"2025-02-21T18:16:37","slug":"inclined-auxetic-metamaterials-buckling","status":"publish","type":"post","link":"https:\/\/research.gsd.harvard.edu\/maps\/2022\/01\/26\/inclined-auxetic-metamaterials-buckling\/","title":{"rendered":"Inclined Auxetic Metamaterials: Buckling"},"content":{"rendered":"\n<p><a href=\"https:\/\/research.gsd.harvard.edu\/maps\/research\/\" data-type=\"page\" data-id=\"2\">Research<\/a><\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Inclined Auxetic Metamaterials: Buckling<\/h1>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"A worm-like robot moves by changing the friction between each segment of its body and the ground\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/0YT-bYogQTg?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"background\">Summary<\/h2>\n\n\n\n<p><span style=\"font-size: 16px;font-family: georgia, palatino\">Our earlier work on <a href=\"https:\/\/research.gsd.harvard.edu\/maps\/portfolio\/alive-exhibition-elastic-surfaces\/\">Auxetic Surfaces<\/a> was based on the in-plane buckling of elastomeric surfaces caused by hinges oriented normal to the base surface. This current work titled Inclined Auxetics: Buckling was an opportunistic approach which arose when the hinges were oriented at an angle (inclined) to the base surface. Based on the nature of the hinges, Inclined Auxetic structures can be further sub-categorized into buckling based and kinematic based.&nbsp;<\/span><\/p>\n\n\n\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69e99dd7b5a63&quot;}\" data-wp-interactive=\"core\/image\" class=\"wp-block-image size-large is-resized wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on-async--click=\"actions.showLightbox\" data-wp-on-async--load=\"callbacks.setButtonStyles\" data-wp-on-async-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/research.gsd.harvard.edu\/maps\/files\/2024\/11\/1-Distinguish-1024x176-1.png\" alt=\"Images showing difference in the hinge orientation between regular auxetic surfaces and inclined auxetic surfaces\" class=\"wp-image-8060\" style=\"width:719px;height:auto\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Enlarge\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on-async--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><figcaption class=\"wp-element-caption\"><span style=\"font-size: 14px\">Difference in the hinge orientation between regular auxetic surfaces and inclined auxetic surfaces<\/span><\/figcaption><\/figure>\n\n\n\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69e99dd7b610c&quot;}\" data-wp-interactive=\"core\/image\" class=\"wp-block-image size-large wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on-async--click=\"actions.showLightbox\" data-wp-on-async--load=\"callbacks.setButtonStyles\" data-wp-on-async-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/research.gsd.harvard.edu\/maps\/files\/2024\/11\/2-SubCatagories-e1643060312622-1024x399-1.png\" alt=\"Two subcatagories of Inclined Auxetics viz. Buckling and kinematic\" class=\"wp-image-8061\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Enlarge\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on-async--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><figcaption class=\"wp-element-caption\"><span style=\"font-size: 14px\">Sub-categories of Inclined Auxetics<\/span><\/figcaption><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Introduction<\/h2>\n\n\n\n<p><span style=\"font-size: 16px;font-family: georgia, palatino\">Our metamaterial is obtained from conceptually slicing an extruded block of elastomer with cylindrical holes (regular auxetic metamaterial at an angle \u03b8).Thin sheets of the same elastomer are used to sea Channels on the top and bottom of the metamaterial are used to vacuum air and deploy it.<\/span><\/p>\n\n\n\n<p>The change in the angle enables the hinges to be inclined causing the buckling to go out-of-plane and hence changing a flat surface to a textured one.<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-vimeo wp-block-embed-vimeo wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Fig1.mp4\" src=\"https:\/\/player.vimeo.com\/video\/669593598?dnt=1&amp;app_id=122963\" width=\"500\" height=\"281\" frameborder=\"0\" allow=\"autoplay; fullscreen; picture-in-picture; clipboard-write; encrypted-media\"><\/iframe>\n<\/div><figcaption class=\"wp-element-caption\">Different values of&nbsp;\u03b8 result in varying levels of out-of-plane deformations.<\/figcaption><\/figure>\n\n\n<div class=\"wp-block-image wp-image-8106 size-full\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69e99dd7b6983&quot;}\" data-wp-interactive=\"core\/image\" class=\"aligncenter wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on-async--click=\"actions.showLightbox\" data-wp-on-async--load=\"callbacks.setButtonStyles\" data-wp-on-async-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/research.gsd.harvard.edu\/maps\/files\/2024\/11\/Web1.jpg\" alt=\"Picture of charts showing how ifferent values of\u00a0\u03b8 result in varying levels of out-of-plane deformations\" class=\"wp-image-8106\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Enlarge\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on-async--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure><\/div>\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-vimeo wp-block-embed-vimeo wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Fig2_DiffAngleDeploy.mp4\" src=\"https:\/\/player.vimeo.com\/video\/669593611?dnt=1&amp;app_id=122963\" width=\"500\" height=\"281\" frameborder=\"0\" allow=\"autoplay; fullscreen; picture-in-picture; clipboard-write; encrypted-media\"><\/iframe>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Simulations<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-vimeo wp-block-embed-vimeo wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Fig6.mp4\" src=\"https:\/\/player.vimeo.com\/video\/669593654?dnt=1&amp;app_id=122963\" width=\"500\" height=\"281\" frameborder=\"0\" allow=\"autoplay; fullscreen; picture-in-picture; clipboard-write; encrypted-media\"><\/iframe>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Properties<\/strong><\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Light Diffusion<\/h3>\n\n\n\n<p><span style=\"font-family: georgia, palatino;font-size: 16px\"><span lang=\"en-US\">Since the buckling-induced textures have identical morphologies, but an out-of-plane amplitude that monotonically increases with&nbsp;\u03b8, below we will only consider the metamaterials with \u03b8=0<\/span><span lang=\"x-IV_mathan\">\u2218<\/span><span lang=\"en-US\">&nbsp;and&nbsp;\u03b8=45<\/span><span lang=\"x-IV_mathan\">\u2218<\/span><span lang=\"en-US\">. These two configurations provide the maximum difference in 3D deformation, and therefore represent the best candidates for demonstrating how the buckling-induced textures can be leveraged to modulate additional functionalities of these metamaterials, such as light diffusion and friction.<\/span><\/span><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69e99dd7b730c&quot;}\" data-wp-interactive=\"core\/image\" class=\"aligncenter wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on-async--click=\"actions.showLightbox\" data-wp-on-async--load=\"callbacks.setButtonStyles\" data-wp-on-async-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/research.gsd.harvard.edu\/maps\/files\/2024\/11\/Light-1024x410-1.jpg\" alt=\"Picture showing light diffusion property of the metamaterial\" class=\"wp-image-8108\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Enlarge\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on-async--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure><\/div>\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-vimeo wp-block-embed-vimeo wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Fig3_LightReflection.mp4\" src=\"https:\/\/player.vimeo.com\/video\/669593623?dnt=1&amp;app_id=122963\" width=\"500\" height=\"281\" frameborder=\"0\" allow=\"autoplay; fullscreen; picture-in-picture; clipboard-write; encrypted-media\"><\/iframe>\n<\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Friction<\/h3>\n\n\n\n<p><span style=\"font-family: georgia, palatino;font-size: 16px\">Changes in&nbsp;surface morphology&nbsp;can also translate into changes in&nbsp;frictional properties of a structure. Beyond the ability of these metamaterials to generate large-scale out-of-plane surface geometries, this behavior also offers the opportunity to expose\/retract a third material, leading to a tunable Coefficient of Friction(\u03bc)For example, if we simply attach small acrylic spheres in the areas of the surface that retract during buckling , such elements (i) dominate the contact properties in the&nbsp;initial configuration&nbsp;and (ii) disengage with the substrate under vacuum, which then comes in contact with the elastomer.<\/span><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69e99dd7b7a79&quot;}\" data-wp-interactive=\"core\/image\" class=\"aligncenter wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on-async--click=\"actions.showLightbox\" data-wp-on-async--load=\"callbacks.setButtonStyles\" data-wp-on-async-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/research.gsd.harvard.edu\/maps\/files\/2024\/11\/Friction-1024x405-1.jpg\" alt=\"\" class=\"wp-image-8111\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Enlarge\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on-async--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure><\/div>\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-vimeo wp-block-embed-vimeo wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Fig4_Friction.mp4\" src=\"https:\/\/player.vimeo.com\/video\/669593632?dnt=1&amp;app_id=122963\" width=\"500\" height=\"281\" frameborder=\"0\" allow=\"autoplay; fullscreen; picture-in-picture; clipboard-write; encrypted-media\"><\/iframe>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Application: Soft Robotic Crawler<\/h2>\n\n\n\n<p><span style=\"font-family: georgia, palatino;font-size: 16px\">To demonstrate friction control, we created a soft crawling robot that harnesses the switchable frictional properties&nbsp;of our&nbsp;metamaterial&nbsp;to achieve locomotion.<\/span><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/research.gsd.harvard.edu\/maps\/files\/2024\/11\/SRC.png\" alt=\"\" class=\"wp-image-8113\" \/><\/figure><\/div>\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-vimeo wp-block-embed-vimeo wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Fig5_Robot.mp4\" src=\"https:\/\/player.vimeo.com\/video\/669593646?dnt=1&amp;app_id=122963\" width=\"500\" height=\"281\" frameborder=\"0\" allow=\"autoplay; fullscreen; picture-in-picture; clipboard-write; encrypted-media\"><\/iframe>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">Attribution<\/h2>\n\n\n\n<p><span style=\"font-family: georgia, palatino;font-size: 16px\">MaP+S Group at Harvard GSD: <em>Saurabh A Mhatre, Olga Mesa and Martin Bechthold.<\/em><\/span><\/p>\n\n\n\n<p><span style=\"font-family: georgia, palatino;font-size: 16px\">Bertoldi Group at Harvard SEAS: <em>Matheus C. Fernandes, Antonio E. Forte, Bing Zhao, James Weaver and Katia Bertoldi.&nbsp;<\/em><\/span><\/p>\n\n\n\n<p><span style=\"font-size: 14px;font-family: georgia, palatino\"><em>This work was supported by&nbsp;<span id=\"GS1\">NSF-GRFP Fellowship<\/span>&nbsp;Grant Number&nbsp;<a href=\"https:\/\/www-sciencedirect-com.ezp-prod1.hul.harvard.edu\/science\/article\/pii\/S2352431621002182#GS1\">DGE-1144152<\/a>&nbsp;(M.C.F.), a&nbsp;<span id=\"GS2\">GEM Consortium Fellowship (M.C.F.)<\/span>&nbsp;and the&nbsp;<span id=\"GS3\">Harvard Graduate Prize Fellowship (M.C.F.)<\/span>, and was partially supported by the NSF through the&nbsp;<span id=\"GS4\">Harvard University Materials Research Science and Engineering Center<\/span>&nbsp;Grant Number&nbsp;<a href=\"https:\/\/www-sciencedirect-com.ezp-prod1.hul.harvard.edu\/science\/article\/pii\/S2352431621002182#GS4\">DMR-2011754<\/a>&nbsp;and&nbsp;<span id=\"GS5\">NSF DMREF<\/span>&nbsp;Grant Number&nbsp;<a href=\"https:\/\/www-sciencedirect-com.ezp-prod1.hul.harvard.edu\/science\/article\/pii\/S2352431621002182#GS5\">DMR-1922321<\/a>. We also thank Mohamed Zanaty for insightful discussions and Bolei Deng for assisting with point tracking algorithm.<\/em><\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Publication<\/h2>\n\n\n<div class=\"wp-block-image wp-image-8281\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69e99dd7b86f4&quot;}\" data-wp-interactive=\"core\/image\" class=\"aligncenter wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on-async--click=\"actions.showLightbox\" data-wp-on-async--load=\"callbacks.setButtonStyles\" data-wp-on-async-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/research.gsd.harvard.edu\/maps\/files\/2024\/11\/Spread-Image-1024x686-1.png\" alt=\"Picture of the work featured on the front cover of Extreme Mechanics Letters journal (Issue 51)\" class=\"wp-image-8281\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Enlarge\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on-async--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><figcaption class=\"wp-element-caption\">Featured on the Front Cover of Extreme Mechanics Letters journal (Issue 51)<\/figcaption><\/figure><\/div>\n\n\n<p><span style=\"font-size: 14px;font-family: georgia, palatino\"><em>Matheus C. Fernandes\u2020, Saurabh Mhatre\u2020, Antonio E. Forte, Bing Zhao, Olga Mesa, James C. Weaver, Martin Bechthold, Katia Bertoldi,<\/em><\/span> <span style=\"font-size: 14px;font-family: georgia, palatino\"><em><a href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S2352431621002182\">Surface texture modulation via buckling in porous inclined mechanical metamaterials.<\/a> Extreme Mechanics Letters, Volume 51,2022,101549,ISSN 2352-4316, https:\/\/doi.org\/10.1016\/j.eml.2021.101549.<\/em><\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Media<\/h2>\n\n\n\n<p><a href=\"https:\/\/www.seas.harvard.edu\/news\/2022\/03\/unexplored-dimensions-porous-metamaterials\">Read more on the website of Harvard School of Engineering and Applied Sciences<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/phys.org\/news\/2022-03-unexplored-dimensions-porous-metamaterials.html\">Read more on Physics.org<\/a><\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\"><\/div>\n<\/div>\n\n\n\n<div style=\"height:100px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>This work was an opportunistic approach which arose when the hinges were oriented at an angle (inclined) to the base surface. Based on the nature of the hinges, Inclined Auxetic structures can be further sub-categorized into buckling based and kinematic based.\u00a0<\/p>\n","protected":false},"author":6,"featured_media":2719,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[9],"tags":[40],"class_list":["post-1230","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-portfolio","tag-adaptive-systems"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Inclined Auxetic Metamaterials: Buckling - MaP+S Group<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/research.gsd.harvard.edu\/maps\/2022\/01\/26\/inclined-auxetic-metamaterials-buckling\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Inclined Auxetic Metamaterials: Buckling - MaP+S Group\" \/>\n<meta property=\"og:description\" content=\"This work was an opportunistic approach which arose when the hinges were oriented at an angle (inclined) to the base surface. 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