\form#0:$\rho$
\form#1:$\rho_s$
\form#2:$E_b$
\form#3:$D_{\omega}(X,T)$
\form#4:$D_T(X,T)$
\form#5:$c$
\form#6:$N$
\form#7:$B$
\form#8:$ K_{aa} = \int_{Omega} B^T D_{\omega} B d\Omega$
\form#9:$ K_{aa} \approx \sum_{t=1}^{N_{IP}} \left( \sqrt{ds^2} \sqrt{det\left( J^T*J \right)} B^T D_{\omega} B \right)\mid_{IP}$
\form#10:$J$
\form#11:$\sqrt{ds^2}$
\form#12:$K_{\omega} = \int_{\Omega} B^T D_{\omega} B d\Omega$
\form#13:$K_{T} = \int_{\Omega} B^T D_{T} B d\Omega$
\form#14:$K_{ab}$
\form#15:$k_{\omega T} = \frac{H}{R T}\frac{\delta\omega}{\delta H}\frac{E_b}{T}$
\form#16:$S$
\form#17:$X_{ref}$
\form#18:$X_{ref}-X$
\form#19:$q$
\form#20:$ q=S\left(X_{ref}-X\right)$
\form#21:\[ \left[\begin{array}{c} f_a \\ f_b \end{array}\right] = \left[\begin{array}{cc} K_{aa}&K_{ab}\\ K_{ba}&K_{bb} \end{array}\right] \left[\begin{array}{c} a \\ b \end{array}\right] + \left[\begin{array}{cc} c_{aa} & c_{ab} \\ c_{ba} & c_{bb} \end{array}\right] \left[\begin{array}{c} \dot{a} \\ \dot{b} \end{array\right]} \]
\form#22:$ MC = \left[ -T \frac{ln(1-h)}{c_2 \left(1-\frac{T}{T_c} \right)^{c_1}}\right]^{\frac{1}{c_3 T^{c_4}}}$
\form#23:$MC$
\form#24:$RH = 1 - \exp{\left(\frac{1}{-T} M^{c_3 T^{c_4}}c_2\left(1-\frac{T}{T_c}\right)^{c_1}\right)} $
\form#25:$\frac{\delta\omega}{\delta H}$
\form#26:$ \frac{\delta\omega}{\delta H}$
\form#27:$J/(Kg K)$
\form#28:$c = \frac{0.0022}{1+0.01*M}*T^2 + \frac{3.32*0.01*M+2.95}{1+0.01M}T+ \frac{4057*0.01M+526}{1+0.01M}$
\form#29:$M$
\form#30:$T$
\form#31:$W/(m K)$
\form#32:$ k_T = 0.19933+0.18888*10^{-3}*(T-293.15)$
\form#33:$ k_L = 0.29937+0.70147*10^{-3}(T-293.15) $
\form#34:$ diag(D_T) = (k_T, k_R, k_L)$
\form#35:$ k_T = 0.1989+0.8313*10^{-4}*(T-293.15)$
\form#36:$ k_L = 0.2991+0.6184*10^{-4}(T-293.15) $