Table 1 Drucker–Prager... | Emerald Publishing

Table 1

Drucker–Prager viscoplastic-damage model

(a) Additive split of the strain tensor
$ϵ = ϵ^{e} + ϵ^{p}$
(b) Elastic constitutive equation
$σ = \frac{\partial ψ}{\partial ϵ^{e}} = (1 - α_{d}) D^{e} : ϵ^{e}$
(c) Yield function
$f (σ, α_{d}) = c_{k}^{2} (\frac{1}{r_{p}^{2}} + \frac{1}{r_{d}^{2}}) - 1$ ⁠; $c_{k} = \frac{(q - c_{3} p)}{(c_{2} p + c_{1})}$
(d) Non-associative flow rule
${\dot{ϵ}}^{p} = \dot{γ} \frac{\partial g}{\partial σ}$ ⁠; $g = q - c_{3} p$ $\dot{γ} = \frac{1}{η} {[q - c_{3} p - (c_{2} p + c_{1}) r_{p} {1 - {[\frac{q - c_{3} p}{(c_{2} p + c_{1}) r_{d}}]}^{2}}^{1 / 2}]}^{1 / (n - 1)}$
(e) Evolution of accumulated plastic strain and damage
${\dot{α}}_{γ} = \dot{γ}$ ${\dot{α}}_{d} = {(\frac{r_{p}}{r_{d}})}^{2} \frac{{\dot{α}}_{γ} (q - c_{3} p)}{(q - c_{3} p - {\dot{α}}_{γ}^{n - 1} η^{n - 1})}$

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