next up previous contents index
Next: 32.1.2 Principal Strains Up: 32.1 Element Strains Previous: 32.1 Element Strains   Contents   Index


32.1.1 Equivalent Von Mises Strain

DIANA calculates the equivalent Von Mises strain according to

$\displaystyle \varepsilon_{{\mathrm{eq}}}^{}$ = $\displaystyle {\tfrac{{2}}{{3}}}$$\displaystyle \sqrt{{ \frac{3 \left( e_{xx}^{2} + e_{yy}^{2} + e_{zz}^{2} \righ...
...ac{3 \left( \gamma_{xy}^{2} + \gamma_{yz}^{2} + \gamma_{zx}^{2} \right )}{4} }}$ (32.3)

With the deviatoric strains:

\begin{displaymath}\begin{split}e_{xx} & = + \tfrac{2}{3}\varepsilon _{xx} - \tf...
...3}\varepsilon _{yy} + \tfrac{2}{3}\varepsilon _{zz} \end{split}\end{displaymath} (32.4)

The engineering strains $ \gamma$ are defined as:

$\displaystyle \gamma_{{ij}}^{}$ = 2 x $\displaystyle \varepsilon_{{ij}}^{}$ (32.5)

For some calculations the strains are placed in a strain matrix E which for the general three-dimensional strain situation is given by

E = $\displaystyle \left[\vphantom{ \negthickspace \begin{array}{ccc} \varepsilon _{...
...zx} & \varepsilon _{yz} & \varepsilon _{zz} \end{array} \negthickspace }\right.$ $\displaystyle \begin{array}{ccc} \varepsilon _{xx} & \varepsilon _{xy} & \varep...
...  [0.5ex] \varepsilon _{zx} & \varepsilon _{yz} & \varepsilon _{zz} \end{array}$ $\displaystyle \left.\vphantom{ \negthickspace \begin{array}{ccc} \varepsilon _{...
...zx} & \varepsilon _{yz} & \varepsilon _{zz} \end{array} \negthickspace }\right]$ (32.6)



DIANA-9.4.4 User's Manual - Analysis Procedures
First ed.

Copyright (c) 2012 by TNO DIANA BV.