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Pol Grasland-Mongrain edited Introduction.tex
over 8 years ago
Commit id: e445ea6cd0559651d2834685e8631cb438f2ab70
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u_z = \frac{(3\lambda + 2\mu)}{(\lambda + 2\mu)} \frac{\alpha E \zeta}{\rho C S \zeta} \approx 3 \alpha \frac{E}{\rho C S}
% \label{eq:deplUnidim}
\end{equation}
as in a biological soft tissues, $\mu \gg \lambda$. Taking as an order of magnitude $\alpha$ = 70.10$^{-6}$ K$^{-1}$ (water linear thermal dilatation coefficient), $E$ = 200 mJ, $\rho$ = 1000 kg.m$^{-3}$ (water density), $C$ = 4180 kg.m$^{-3}$ (water calorific capacity) and $S$ = 20 mm$^2$, we obtain a displacement $u_z$= 0.5 $\mu$m. This value is
still slightly smaller than the typical
displacement ultrasound resolution
with ultrasound, of displacement, typically of a few micrometers.
This unidimensional analysis cannot explain the induction of shear waves in a thermoelastic expansion, as this displacement is curl-free. However, in In a tridimensional model,
displacements along X and Y axis would also occurs, as the local expansion acts as dipolar forces parallel to the
surface, so displacements along X and Y axis could also lead to shear waves. surface.
In the ablative regime, the local increase of temperature is so high that the surface of the medium is vaporized. This phenomenon creates a stress $\sigma$ in the medium, given by \cite{scruby1990laser}:
\begin{equation}
...