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Pol Grasland-Mongrain edited Simu disp maps.tex
over 8 years ago
Commit id: 7f143dd6d77a7d0a59d9706101101027421b06f6
deletions | additions
diff --git a/Simu disp maps.tex b/Simu disp maps.tex
index 5ca3817..0b750b4 100644
--- a/Simu disp maps.tex
+++ b/Simu disp maps.tex
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u_z = \frac{\zeta}{\rho \lambda}\frac{I^2}{(L+C(T_V-T_0))^2}
\label{eq:deplAblaApprox}
\end{equation}
Using high-energy experimental parameter, $\zeta \approx \gamma^{-1} = 40 \mu$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) and $T_V-T_0$ = 373-298 = 75 K, we obtain a displacement $u_z$ approximately equal to 2.9 $\mu$m. While slightly higher, this value is in good agreement with experimental displacement (2.5 $\mu$m). It is directed inside the medium,
in agreement with the experimental images as
illustrated indicated by the white circle in the figure \ref{figElastoPVA}-(B).
To calculate the propagation of the displacement along space and time, we modeled the ablation regime as a point force directed along Z direction with a depth of 40 $\mu$m and of constant value from -2.5 to 2.5 mm. The magnitude of the force is stored in a matrix $H_z^{abla}(y,z,t)$. Propagation as a shear wave was calculated using Green operators $G_{zz}$ \cite{aki1980quantitative}:
\begin{equation}