{"id":10453,"date":"2022-08-09T14:28:03","date_gmt":"2022-08-09T18:28:03","guid":{"rendered":"https:\/\/www.purdue.edu\/freeform\/me323\/?page_id=10453"},"modified":"2022-08-09T14:28:03","modified_gmt":"2022-08-09T18:28:03","slug":"poissons-ratio","status":"publish","type":"page","link":"https:\/\/www.purdue.edu\/freeform\/me323\/animations-and-demonstrations\/poissons-ratio\/","title":{"rendered":"Poisson&#8217;s ratio"},"content":{"rendered":"<p><em><strong><span style=\"font-size: 18pt\">Uniaxial loading<\/span><\/strong><\/em><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-9132 aligncenter\" src=\"https:\/\/www.purdue.edu\/freeform\/me323\/wp-content\/uploads\/sites\/2\/2021\/08\/positive_poisson-1-249x300.jpg\" alt=\"\" width=\"249\" height=\"300\" srcset=\"https:\/\/www.purdue.edu\/freeform\/me323\/wp-content\/uploads\/sites\/2\/2021\/08\/positive_poisson-1-249x300.jpg 249w, https:\/\/www.purdue.edu\/freeform\/me323\/wp-content\/uploads\/sites\/2\/2021\/08\/positive_poisson-1.jpg 382w\" sizes=\"auto, (max-width: 249px) 100vw, 249px\" \/><\/p>\n<ul>\n<li>Tensile\/compressive stress in the <em>x<\/em>-direction produces tensile\/compressive strain in the <em>x<\/em>-direction, with the stress and strain related through Young&#8217;s modulus <em>E<\/em>:<\/li>\n<li>Strain in the <em>x<\/em>-direction produces strains the <em>y<\/em>&#8211; and <em>z<\/em>-directions. The strains in the <em>y<\/em>&#8211; and <em>z<\/em>-directions are proportional to the strain in the x-direction through the negative of the Poisson&#8217;s ratio.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p><em><strong><span style=\"font-size: 14pt\">Positive Poisson&#8217;s ratio<\/span><\/strong><\/em><br \/>\nIf the Poisson&#8217;s ratio of the material if positive, then tensile\/compressive strains in the x-direction produce compressive\/tensile strains in the y- and z-directions, as shown below.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" style=\"border: 1px solid #000000\" src=\"https:\/\/www.purdue.edu\/freeform\/me323\/wp-content\/uploads\/sites\/2\/2021\/06\/threed_stress_strain.gif\" width=\"265\" height=\"245\" \/><\/p>\n<p>&nbsp;<\/p>\n<p><em><strong><span style=\"font-size: 14pt\">Negative Poisson&#8217;s ratio<\/span><\/strong><\/em><br \/>\nIf the Poisson&#8217;s ratio of the material if positive, then tensile\/compressive strains in the x-direction produce tensile\/compressive strains in the y- and z-directions, just the opposite of that for a positive Poisson&#8217;s ratio.<\/p>\n<p><em><u>QUESTION<\/u><\/em>: Can a material possess a negative Poisson\u2019s ratio? The answer is \u201cyes\u201d. Such materials are known as \u201c<strong><em>auxetic materials<\/em><\/strong>\u201d. From above, we see than an auxetic material will expand in the transverse directions for a tensile axial load. Consider the animation below of such a material, and study how a negative value for Poisson&#8217;s ratio is possible with this material. As can be seen here, a compressive axial load produces contraction in the transverse direction, and a tensile axial load produces expansion in the transverse direction.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" style=\"border: 1px solid #000000\" src=\"https:\/\/www.purdue.edu\/freeform\/me323\/wp-content\/uploads\/sites\/2\/2021\/08\/negative_poissons_ratio.gif\" width=\"674\" height=\"415\" \/><\/p>\n<p>There are a number of types of polyurethane foam materials with cell structures resembling the structure shown above. Kevlar woven composite materials used for body armor are also auxetic materials.<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Uniaxial loading Tensile\/compressive stress in the x-direction produces tensile\/compressive strain in the x-direction, with the stress and strain related through Young&#8217;s modulus E: Strain in the x-direction produces strains the y&#8211; and z-directions. The strains in the y&#8211; and z-directions are proportional to the strain in the x-direction through the negative of the Poisson&#8217;s ratio. &hellip; <a href=\"https:\/\/www.purdue.edu\/freeform\/me323\/animations-and-demonstrations\/poissons-ratio\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Poisson&#8217;s ratio<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":10,"featured_media":0,"parent":5074,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-10453","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/pages\/10453","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/users\/10"}],"replies":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/comments?post=10453"}],"version-history":[{"count":1,"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/pages\/10453\/revisions"}],"predecessor-version":[{"id":10678,"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/pages\/10453\/revisions\/10678"}],"up":[{"embeddable":true,"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/pages\/5074"}],"wp:attachment":[{"href":"https:\/\/www.purdue.edu\/freeform\/me323\/wp-json\/wp\/v2\/media?parent=10453"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}