Added ref for poroelastodynamic and update formulation

Author: rezgarshakeri

docs/references.bib

@@ -105,6 +105,16 @@ @Article{Day:Ely:2002
   doi = 	 {10.1785/0120010273}
 }
 
+@article{ding2013fundamental,
+  title={Fundamental solutions of poroelastodynamics in frequency domain based on wave decomposition},
+  author={Ding, Boyang and Cheng, Alexander H-D and Chen, Zhanglong},
+  journal={Journal of Applied Mechanics},
+  volume={80},
+  number={6},
+  year={2013},
+  publisher={American Society of Mechanical Engineers Digital Collection}
+}
+
 @Article{Drucker:Prager:1952,
   author = 	 {Drucker, D.~C. and Prager, W.},
   title = 	 {Soil mechanics and plastic analysis for limit design},

docs/user/governingeqns/poroelasticity/dynamic.md

@@ -36,8 +36,12 @@ We replace the variation of fluid content variable, $\zeta$, with its definition
   \frac{\dot{p}}{M} = \gamma \left(\vec{x},t \right) - \alpha \left( \nabla \cdot \dot{\vec{u}} \right) -\nabla \cdot \vec{q}.
 \end{gather}
 %
-We write the volumetric strain in terms of displacement, because this dynamic formulation does not include the volumetric strain as an unknown.
-
+We write the volumetric strain in terms of displacement, because this dynamic formulation does not include the volumetric strain as an unknown. Note that for poroelastodynamics we use the generalized Darcy's law {cite}`ding2013fundamental` as
+%
+\begin{equation}
+  \vec{q}(p) = -\frac{\boldsymbol{k}}{\mu_{f}}(\nabla p + \rho_{f} \frac{\partial \vec{v}}{\partial t} - \vec{f}_f).
+\end{equation}
+%
 Using trial functions ${\vec{\psi}_\mathit{trial}^{u}}$, ${\psi_\mathit{trial}^{p}}$, and ${\vec{\psi}_\mathit{trial}^{v}}$, and incorporating the Neumann boundary conditions, the weak form may be written as:
 %
 \begin{align}

docs/user/governingeqns/poroelasticity/index.md

@@ -44,7 +44,7 @@ For this case, we will assume that the material properties are isotropic, result
 %
 \begin{equation}
   \boldsymbol{\sigma}(\vec{u},p) = \boldsymbol{C}:\boldsymbol{\epsilon} - \alpha p \boldsymbol{I}
-  = \lambda \boldsymbol{I} \epsilon_{v} + 2 \mu - \alpha \boldsymbol{I} p
+  = \lambda \boldsymbol{I} \epsilon_{v} + 2 \mu  \boldsymbol{\epsilon} - \alpha \boldsymbol{I} p
 \end{equation}
 %
 where $\lambda$ and $\mu$ are Lamé's parameters, $\lambda = K_{d} - \frac{2 \mu}{3}$, $\mu$ is the shear modulus, and the volumetric strain is defined as $\epsilon_{v} = \nabla \cdot \vec{u}$.