diff --git a/docs/references.bib b/docs/references.bib index 3c0424b343..0cc9bdc9ac 100644 --- a/docs/references.bib +++ b/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}, diff --git a/docs/user/governingeqns/poroelasticity/dynamic.md b/docs/user/governingeqns/poroelasticity/dynamic.md index 3853e8ee0a..3811344231 100644 --- a/docs/user/governingeqns/poroelasticity/dynamic.md +++ b/docs/user/governingeqns/poroelasticity/dynamic.md @@ -37,7 +37,13 @@ We replace the variation of fluid content variable, $\zeta$, with its definition \end{gather} % 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 - \vec{f}_f + \rho_{f} \frac{\partial \vec{v}}{\partial t}), +\end{equation} +% +where the generalized Darcy's law adds the term $\rho_{f} \frac{\partial \vec{v}}{\partial t}$. 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} diff --git a/docs/user/governingeqns/poroelasticity/index.md b/docs/user/governingeqns/poroelasticity/index.md index a8c67be067..5e4d7b4efe 100644 --- a/docs/user/governingeqns/poroelasticity/index.md +++ b/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 $\epsilon_{v} = \nabla \cdot \vec{u}$.