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<a name = "hj-top"> </a><table class = "table1" id = "table11"><tr><td><table class = "DocHeader"><tr><td class = "DocHeader1" colspan = "2"><h1>Effects of Nonlinear Material Laws</h1></td></tr><tr><td class = "DocHeader4" colspan = "2"/></tr><tr><td class = "DocHeader3" colspan = "2"><table class = "DocThemeIntro" id = "table12"><tr><td class = "Intro1Only"><p class = "header"><p class = "abstract"> 
   <span class = "shortdesc"> This section describes the effects of nonlinear material laws that are taken into
      account during a structural analysis. The effects are shown using examples that are referenced
      in the <span class = "ph">Tosca Structure</span> Examples Guide. </span>
 
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<p>This page discusses: </p><ul><li><a href = "#tso-c-usr-sizing-NonLin-Effects-Material__" id = "toc_rg" title = "">Elastic-Plastic Material with a Bending Plate</a></li><li><a href = "#tso-c-usr-sizing-NonLin-Effects-Material__" id = "toc_rg" title = "">See Also</a></li></ul>
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   <div class = "section"><h2 class = "title sectiontitle">Elastic-Plastic Material with a Bending Plate</h2>  <br/><img class = "image" src = "../TsoExampleImages/sizingPlasticPlateModel.png" width = "378"/><br/> A vertical plate has one edge encastered and the opposite
      edge subjected to a load F in the negative Y-direction. In two scenarios, the material is
      chosen to be elastic and elastic-plastic, respectively. In the elastic material, the maximum
      stress occurs at the two encastered corners, while in the elastic-plastic material the effect
      of yielding increases the region of maximum stress across an envelope around the encastered
      corners. Seen in the graphic below. <br/><img class = "image" src = "../TsoUserImages/NonLinSizing_Effects-Material-Stress.jpg" width = "756"/><br/> By taking a thin strip from the left side of the plate, it
      can be sees that with elastic-plastic material the stresses are leveled in the outer regions
      (below, right side). This is because of the yielding effect where stress does not increase
      with increasing strain. On the contrary with elastic material, the stresses scale linearly
      across the plate and reach higher values at the boundaries. <br/><img class = "image" src = "../TsoUserImages/NonLinSizing_Effects-Material-MaxStress.jpg" width = "680"/><br/> </div>
 
   <div class = "section"><p><map name = "FPMap1"><area href = "#hj-top" title = "Back to Top" shape = "rect" coords = "416, 0, 435, 10"/></map><span class = "itemsprite"/></p><h2 class = "title sectiontitle">See Also</h2> 
     The optimization for this example and further
    explanations can be found in the <span class = "ph">Tosca Structure</span> Examples Guide (see 
    <a class = "xref" href = "../TsoExampleMap/tso-m-example-sizing-NonLinExamples-Plastic-sb.htm#tso-m-example-sizing-NonLinExamples-Plastic-sb" title = "Some applications of nonlinear material laws are described within this section.">Examples with Nonlinear Material Laws</a>).
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