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7 changes: 6 additions & 1 deletion docs/user/governingeqns/elasticity/nondimensionalization.md
Original file line number Diff line number Diff line change
Expand Up @@ -54,7 +54,12 @@ Considering isotropic, linear elasticity we have
\boldsymbol{\sigma} = \boldsymbol{C} : \boldsymbol{\epsilon} = \boldsymbol{C} : \frac{1}{2}\left(\boldsymbol{\nabla} + \boldsymbol{\nabla}^T \right) \vec{u}.
\end{equation}
%
Substituting in our nondimensional values yields
We define
%
\begin{equation}
C^* = \frac{C}{\mu_o},
\end{equation}
and substituting yields
%
\begin{equation}
\sigma_o \boldsymbol{\sigma}^* = \mu_o \boldsymbol{C}^* : \frac{u_o}{x_o} \frac{1}{2}\left(\boldsymbol{\nabla}^* + \boldsymbol{\nabla}^{*^T}\right) \vec{u}^*.
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Original file line number Diff line number Diff line change
Expand Up @@ -69,7 +69,7 @@ It also separates the stress scale used to nondimensionalize stress, tractions,
| $u_o$ | Displacement scale |
| $\mu_o$ | Rigidity scale |
| $t_o$ | Time scale |
| $\sigma_o = p_o = \mu_o \frac{u_o}{x_o}$ | Stress scale |
| $\sigma_o = p_o = \mu_o \frac{u_o}{x_o}$ | Stress and pressure scale |
| $f_o = \frac{\sigma_o}{x_o}$ | Body force scale |
| $\rho_o = \mu_o \frac{t_o^2}{x_o^2}$ | Density scale |
```
Original file line number Diff line number Diff line change
Expand Up @@ -134,7 +134,7 @@ It also separates the stress scale used to nondimensionalize stress, tractions,
| $u_o$ | Displacement scale |
| $\mu_o$ | Rigidity scale |
| $t_o= \frac{\mu_{f_o}}{\boldsymbol{k}_o} \frac{x_o^2}{\mu_o}$ | Time scale |
| $\sigma_o = p_o = \mu_o \frac{u_o}{x_o}$ | Stress scale |
| $\sigma_o = p_o = \mu_o \frac{u_o}{x_o}$ | Stress and pressure scale |
| $f_o = \frac{\sigma_o}{x_o}$ | Body force scale |
| $\rho_o = \mu_o \frac{t_o^2}{x_o^2}$ | Density scale |
| $q_o = \frac{u_o}{t_o} $ | Flow scale |
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