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Pol Grasland-Mongrain edited Simu disp maps.tex
over 8 years ago
Commit id: 21801bcd86fd4a540bb439acb9325292b8c5af1a
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diff --git a/Simu disp maps.tex b/Simu disp maps.tex
index 6208aff..c7f7afe 100644
--- a/Simu disp maps.tex
+++ b/Simu disp maps.tex
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\end{equation}
As in a biological soft tissues, $\mu \ll \lambda$, the displacement can be approximated as:
\begin{equation}
u_z = \frac{\zeta}{\rho
\lambda}\frac{I}{(L+C(T_V-T_0))^2} \lambda}\frac{I^2}{(L+C(T_V-T_0))^2}
\label{eq:deplAblaApprox}
\end{equation}. Estimating $\zeta$ equal to 50 $\mu$m (average depth of absorption), $\lambda$ = 2 GPa (first Lamé's coefficient of water), $L$ = 2.2 MJ.kg$^{-1}$ (vaporization latent heat of water), $C$ = 4180 J.kg$^{-1}$.K$^{-1}$ (water heat capacity), $T_V-T_0$ = 373-293 = 80 K (water vaporization temperature minus laboratory temperature), $\rho$ = 1000 kg.m$^{-3}$ (water density), $E$ = 200 mJ, $S$ = 20 mm$^2$ and $\tau$ = 10 ns, we obtain a displacement $u_z$ approximately equal to 3.9 $\mu$m. This is in the order of magnitude of the experimental measured displacement (2 $\mu$m).