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DEFORMATION_PLASTICITY.html
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DEFORMATION_PLASTICITY.html
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<html><head><link rel="stylesheet" type="text/css" href="style.css"/></head><body> <H2> <BR> *DEFORMATION PLASTICITY </H2> <P> Keyword type: model definition, material <P> This option defines the elasto-plastic behavior of a material by means of the generalized Ramberg-Osgood law. The one-dimensional model takes the form: <P> <P></P> <DIV ALIGN="CENTER" CLASS="mathdisplay"><!-- MATH \begin{equation} E\epsilon=\sigma + \alpha \left( \frac {\left| \sigma \right| }{\sigma_0} \right)^{n-1}\sigma \end{equation} --> <TABLE CLASS="equation" CELLPADDING="0" WIDTH="100%" ALIGN="CENTER"> <TR VALIGN="MIDDLE"> <TD NOWRAP ALIGN="CENTER"><SPAN CLASS="MATH"><IMG WIDTH="169" HEIGHT="61" ALIGN="MIDDLE" BORDER="0" SRC="img2326.png" ALT="$\displaystyle E\epsilon=\sigma + \alpha \left( \frac {\left\vert \sigma \right\vert }{\sigma_0} \right)^{n-1}\sigma$"></SPAN></TD> <TD NOWRAP CLASS="eqno" WIDTH="10" ALIGN="RIGHT"> (<SPAN CLASS="arabic">700</SPAN>)</TD></TR> </TABLE></DIV> <BR CLEAR="ALL"><P></P> where <SPAN CLASS="MATH"><B><IMG WIDTH="10" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="img247.png" ALT="$ \epsilon$"></B></SPAN> is the logarithmic strain and <SPAN CLASS="MATH"><B><IMG WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="img1293.png" ALT="$ \sigma$"></B></SPAN> the Cauchy stress. In the present implementation, the Eulerian strain is used, which is very similar to the logarithmic strain (about 1.3 % difference dat 20 % engineering strain). All coefficients may be temperature dependent. <P><P> <BR> <P> First line: <UL> <LI>*DEFORMATION PLASTICITY </LI> </UL> <P> Following line: <UL> <LI>Young's modulus (E). </LI> <LI>Poisson's ratio (<SPAN CLASS="MATH"><B><IMG WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0" SRC="img75.png" ALT="$ \nu$"></B></SPAN>). </LI> <LI>Yield stress (<SPAN CLASS="MATH"><B><IMG WIDTH="20" HEIGHT="29" ALIGN="MIDDLE" BORDER="0" SRC="img2327.png" ALT="$ \sigma_0$"></B></SPAN>) </LI> <LI>Exponent (n). </LI> <LI>Yield offset (<SPAN CLASS="MATH"><B><IMG WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" SRC="img138.png" ALT="$ \alpha$"></B></SPAN>). </LI> <LI>Temperature. </LI> </UL> Repeat this line if needed to define complete temperature dependence. <P> <PRE>
Example:
*DEFORMATION PLASTICITY
210000.,.3,800.,12.,0.4
</PRE> <P> defines a Ramberg-Osgood law. No temperature dependence is introduced. <P> <P><P> <BR> Example files: beampl. <P> </body></html>