Table 1. Summary of model equations and... | Emerald Publishing

Table 1.

Summary of model equations and internal state variables

Model component	Equations
Model's internal state	$η_{y}$ ⁠, $D^{p}$ and $I$ with
variables (⁠ $X_{s}$ ⁠)	$η_{y} = M - D^{p} (1 - N)$ $I = D {\dot{ε}}_{q} \sqrt{ρ_{s} / p'}$
Yield surface	$F = q - p' η_{y}$
Plastic potential	$P = q + p' D^{p}$
Hardening rule	$D^{p} = D_{min}^{p} h ε_{q}^{p} \exp (1 - h ε_{q}^{p})$
Strain-rate hardening rule	$D_{min}^{p} / D_{{min}_{0}}^{p} = (I / I_{0})^{κ_{D}}$
Elasticity	$G / G_{0} = (I / I_{0})^{κ_{G}}$
	$K / K_{0} = (I / I_{0})^{κ_{K}}$

Model component	Equations
Model's internal state	$η_{y}$ , $D^{p}$ and $I$ with
variables ( $X_{s}$ )	$η_{y} = M - D^{p} (1 - N)$ $I = D {\dot{ε}}_{q} \sqrt{ρ_{s} / p'}$
Yield surface	$F = q - p' η_{y}$
Plastic potential	$P = q + p' D^{p}$
Hardening rule	$D^{p} = D_{min}^{p} h ε_{q}^{p} \exp (1 - h ε_{q}^{p})$
Strain-rate hardening rule	$D_{min}^{p} / D_{{min}_{0}}^{p} = (I / I_{0})^{κ_{D}}$
Elasticity	$G / G_{0} = (I / I_{0})^{κ_{G}}$
	$K / K_{0} = (I / I_{0})^{κ_{K}}$