Anand Model

The Anand model is available in the form

{\dot{\bar{ε}}}^{c r} = A {[\sinh (ξ \frac{\tilde{q}}{s})]}^{n} \exp (- \frac{Q}{R (θ - θ^{Z})}),

where

${\dot{\bar{ε}}}^{c r}$: is the uniaxial equivalent creep strain rate, $\sqrt{\frac{2}{3} {\dot{ε}}^{c r} : {\dot{ε}}^{c r}},$
$\tilde{q}$: is the uniaxial equivalent deviatoric stress,
$R$: is the universal gas constant,
$θ$: is the temperature,
$θ^{Z}$: is the user-defined value of absolute zero on the temperature scale used,
$Q$: is the activation energy,
$s$: is the deformation resistance, and
$A$ , $m$ , and $ξ$: are material parameters.

The evolution equation for the deformation resistance, $s$ (initially $s = s_{0}$ ), is

\dot{s} = h_{0} {| 1 - \frac{s}{s^{*}} |}^{a} s i g n (1 - \frac{s}{s^{*}}) {\dot{\bar{ε}}}^{c r},

with

s^{*} = \hat{s} {[\frac{1}{A} {\dot{\bar{ε}}}^{c r} \exp (\frac{Q}{R (θ - θ^{Z})})]}^{n},

where

h_{0} = A_{0} + A_{1} (θ - θ^{Z}) {+ A}_{2} {(θ - θ^{Z})}^{2} {+ A}_{3} {\dot{\bar{ε}}}^{c r} {+ A}_{4} {({\dot{\bar{ε}}}^{c r})}^{2},

and

a

n

\hat{s}

A_{0}

A_{1}

A_{2}

A_{3}

, and

A_{4}

are material parameters.

In addition, the initial deformation resistance is a function of temperature of the form

s_{0} = S_{1} + S_{2} (θ - θ^{Z}) {+ S}_{3} {(θ - θ^{Z})}^{2},

where

S_{1}

S_{2}

, and

S_{3}

are the material parameters.