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      <title>Material properties</title>
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      <div class="title_topic5" id="xps10_pagetitle">Material properties</div>
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               <p class="para_td"> <a class="links" href="javascript:void(0)" onclick="top.openFile('sheetmetaldes/smfea_metaform.html');return(false);">MetaForm Overview</a></p>
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               <p class="para_td">Options</p>
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               <p class="para_td"><a class="links" href="javascript:void(0)" onclick="top.openFile('sheetmetaldes/metaform_tips.html');return(false);">Related Topics</a></p>
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      </table><br><p class="para_topic">Material characteristics are represented using a stress&ndash;strain diagram. Due to the large displacements that may occur during a forming analysis, MetaForm accounts for the transition from the elastic domain of the material into the plastic domain. Two distinct linear segments represent the elastic&ndash;plastic relationship, as shown below. The first linear segment, with slope E (the <b class="uiTerm">Elastic Modulus</b>), represents material behavior in the elastic range. The second linear segment, with slope ET (the <b class="uiTerm">Tangent Modulus</b>), represents material behavior in the plastic range.
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         <p align="center"><img align="bottom" src="graphics/meta_elastic.gif"></p>
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      <div class="title_figure">Elastic&ndash;Plastic Stress&ndash;Strain Relationship</div>
      <p class="para_topic">With this model, the stress&ndash;strain relationship will be defined as follows:</p>
      <p align="center"><img align="bottom" src="graphics/meta_code.gif"></p>
      <p class="para_topic">The <b class="uiTerm">Material Properties</b> dialog box lets you specify the following:
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               <p class="para_td">Yield Stress</p>
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               <p class="para_td">The stress at which the material transitions from the elastic behavior of a material to plastic behavior. Typically, the elastic strength of a material is significantly larger than the plastic behavior. &nbsp;However, the behavior of some materials (composites, rubber, etc.) may behave in a manner that contradicts this assumption. You should determine the most appropriate strength values MetaForm should use during the forming analysis. This is also called the <b class="uiTerm">Elastic Limit</b>. Use units of psi (English) or KPa (Metric).
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               <p class="para_td">Elastic Modulus</p>
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               <p class="para_td">Also known as, <b class="uiTerm">Modulus of Elasticity</b>, Young's Modulus. &nbsp;This represents the linear relationship between stress and strain, such that  <img align="bottom" src="graphics/meta1.gif" border="0">. This condition is valid for values of stress that remain below the yield stress of the materials. Use units of psi (English) or KPa (Metric).
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               <p class="para_td">Tangent Modulus</p>
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               <p class="para_td">Represents a linear relationship between stress and strain that is valid for values of stress that exceed the yield stress of the material. Use units of psi (English) or KPa (Metric).</p>
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               <p class="para_td">Poisson's Ration</p>
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               <p class="para_td">The ratio of lateral strain to longitudinal strain.</p>
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               <p class="para_td">r&ndash;Value</p>
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               <p class="para_td">The r&ndash;value is a material property that represents resistance to thinning. Higher r&ndash;values represent higher resistance to thinning when the material is being stretched or resistance to thickening when the material is being compressed. The default value of 1.0 corresponds to a homogeneous material.</p>
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               <p class="para_td">Thickness</p>
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               <p class="para_td">The material thickness used in forming analysis. The thickness must be greater than zero (even when forming sheet bodies).</p>
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               <p class="para_td">Reverse Thickness Direction</p>
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               <p class="para_td">This option lets you reverse the vector that indicates where the material is in relation to the selected region boundary.</p>
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               <p class="para_td">Neutral Offset</p>
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               <p class="para_td">The neutral offset represents the offset distance that is applied to the MetaForm mesh during an analysis. &nbsp;This offset is specified as a ratio of the thickness (for example, a value of 0.5 represents a value &nbsp;½ the thickness). Acceptable values for the neutral offset are between 0.0 and 1.0.</p>
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      </table><br><div class="title_division">Elastic&ndash;plastic behavior</div>
      <p class="para_division">During a <b class="uiTerm">MetaForm Analysis</b> large displacements can occur that result in a transition from the elastic domain of the material into the plastic domain. The approximation of this elastic&ndash;plastic relationship utilizes a quasi&ndash;linear approach, such that two distinct linear segments are used to approximate this stress&ndash;strain relationship as shown in the figure below. The first linear segment will represent material behavior in the elastic range. The slope of this linear domain is represented by the <b class="uiTerm">Elastic Modulus (E)</b>. The slope of this linear plastic domain is represented by the Tangent Modulus (<img align="bottom" src="graphics/meta2.gif" border="0">).
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         <p align="center"><img align="bottom" src="graphics/meta3.gif"></p>
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      <div class="title_figure">Elastic&ndash;Plastic Stress&ndash;Strain Relationship</div>
      <p class="para_division">With this model, a <b class="uiTerm">MetaForm Analysis</b> determines the stress&ndash;strain relationship for each element as follows:
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      <div class="title_division">Poisson's ratio and r&ndash;factor</div>
      <p class="para_division">When a deformable body is subjected to an axial tensile force, not only does it elongate but it also contracts laterally.&nbsp;Likewise, an axial compressive force acting on a body causes it to contract in the direction of the force and its sides expand laterally.&nbsp;The proportional ratio of these strains is referred to as Poisson's ratio ( ), such that for an isotropic material we have:</p>
      <p align="left"><img align="bottom" src="graphics/meta4.gif"></p>
      <p class="para_division">In a <b class="uiTerm">MetaForm Analysis</b>, however, you may consider an anisotropic relationship between the value for Piosson's ratio that is applied in the tangential directions of the element versus the normal direction of the element. This normal anisotropic ratio, or r&ndash;factor, will then be imposed that satisfies the following relationship:
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      <p align="left"><img align="bottom" src="graphics/meta5.gif"></p>
      <p class="para_division">For an isotropic r&ndash;value, (r = 1.0), the volume&ndash;preserving material, the value for Poisson's ratio is:</p>
      <p align="left"><img align="bottom" src="graphics/meta6.gif"></p>
      <p class="para_division">Thus for a given isotropic value for Poisson's ratio, the following relationship will be established to compute equivalent anisotropic values using the R&ndash;value provided, such that the following relationship is obtained:</p>
      <p align="left"><img align="bottom" src="graphics/meta7.gif"></p>
      <p class="para_division">Solving this quadratic equation for  <img align="bottom" src="graphics/meta8.gif" border="0"> and  <img align="bottom" src="graphics/meta9.gif" border="0">, we have:
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      <p align="left"><img align="bottom" src="graphics/meta10.gif"></p>
      <p class="para_division">Thus, when defining the stiffness of each element, the value for Poisson's ratio in the tangential direction,<img align="bottom" src="graphics/meta9.gif" border="0">, is used.
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