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Table 1 Default parameters used in the simulation

From: Enriched continuum for multi-scale transient diffusion coupled to mechanics

ParameterSymbolValueUnits
RVE length\( \ell \)1.0(mm)
Inclusion diameter\( \ell _i \)0.3(mm)
Inclusion volume fraction\( V_{f_i} \)\( \sim \) 0.5 
Maximum attainable concentration in inclusion [42]\( c_{\max } \)24,161(\(\hbox {mol m}^{-3}\))
Minimum attainable concentration in inclusion [42]\( c_0 = 0.19 c_{\max } \)4590.59(\(\hbox {mol m}^{-3}\))
Absolute temperature\( T_0 \)298(K)
Boltzmann constant\( k_b \)\(1.3806\times 10^{-23}\)(\(\hbox {m}^{2}\, \hbox {kg s}^{-2} \, \hbox {K}^{-1}\))
Inclusion chemical modulus [28]\( \Lambda _i = k_b T_0 / c_0\)10,202(\(\hbox {J m}^{-3}/(\hbox {mol m}^{-3})^2 \))
Maximum chemical potential in inclusion\( \mu _{\max }=\Lambda _i(c_{\max }-c_0)\)\(1.99\times 10^{8}\)(\(\hbox {J }/ \hbox {m}^{-3}/(\hbox {mol m}^{-3} )\))
Matrix diffusivity [28]\( {\mathcal {D}}_m \)\(6\times 10^{-11}\)(\(\hbox {m}^{2}\, \hbox {s}^{-1}\))
Inclusion diffusivity [28]\( {\mathcal {D}}_i \)\(1\times 10^{-16}\)(\(\hbox {m}^{2}\, \hbox {s}^{-1}\))
Matrix characteristic time\( t_m = \frac{\ell ^2}{{\mathcal {D}}_m} \)\(1.6\times 10^{4}\)(s)
Inclusion characteristic time\( t_i = \frac{\ell _i^2}{{\mathcal {D}}_i} \)\(3\times 10^{12}\)(s)
Matrix Young’s modulus [42]\( E_m \)1(GPa)
Inclusion Young’s modulus [42]\( E_i \)10(GPa)
Poisson’s ratio [42]\( \nu _m\ \& \ \nu _i \)0.3 
Inclusions partial molar volume [42]\( \gamma \)\(3.497 \times 10^{-6}\)(\(\hbox {m}^{-3}\, \hbox {mol}^{-1}\))
Number of elements 25,498 TRI3 
Number of nodes 12,494 
Total loading timeT\( 0.1 t_i \)(s)
Loading frequency\( \omega \)1(Hz)