Hoffman criterion

II.1.10.16 Hoffman criterion

The Hoffman criterion is very similar to the Tsai-Wu criterion. Only the last term of failure index is different:

\begin{matrix} F I^{Hoffman} = \frac{σ_{11}^{2}}{σ_{11}^{t,all} σ_{11}^{c,all}} + \frac{σ_{22}^{2}}{σ_{22}^{t,all} σ_{22}^{c,all}} + {(\frac{τ_{12}}{τ_{12}^{all}})}^{2} + (\frac{1}{σ_{11}^{t,all}} - \frac{1}{σ_{11}^{c,all}}) σ_{11} \\ + (\frac{1}{σ_{22}^{t,all}} - \frac{1}{σ_{22}^{c,all}}) σ_{22} - \frac{σ_{11} σ_{22}}{σ_{11}^{t,all} σ_{11}^{c,all}} . & (II.1.131) \end{matrix}

Ply passes the failure criterion if

F I^{Hoffman} \leq 1 .

In some of the terms of previous expression the components of Cauchy stress tensor appear linearly, and other terms, they appear quadratically. Therefore, the reserve factor expression is a little more complicated. FeResPost calculates it as follows:

a = \frac{σ_{11}^{2}}{σ_{11}^{t,all} σ_{11}^{c,all}} + \frac{σ_{22}^{2}}{σ_{22}^{t,all} σ_{22}^{c,all}} + {(\frac{τ_{12}}{τ_{12}^{all}})}^{2} - \frac{σ_{11} σ_{22}}{σ_{11}^{t,all} σ_{11}^{c,all}},

b = (\frac{1}{σ_{11}^{t,all}} - \frac{1}{σ_{11}^{c,all}}) σ_{11} + (\frac{1}{σ_{22}^{t,all}} - \frac{1}{σ_{22}^{c,all}}) σ_{22},

c = - 1,

R F^{Hoffman} = \frac{- b + \sqrt{b^{2} - 4 a c}}{2 \cdot F o S \cdot a},

and the strength ratio is given by:

S R^{Hoffman} = \frac{1}{R F^{Hoffman}} .

This criterion is referred to as “Hoffman” criterion in FeResPost.

[next] [prev] [prev-tail] [front] [up]