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Pol Grasland-Mongrain edited Introduction.tex
over 8 years ago
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In the thermoelastic regime, a local dilatation of the medium occurs. In an unbounded solid, this would lead to a curl-free displacement, so no shear wave would occur. However, in the case presented, the solid is semi-infinite (the laser beam is absorbed on one side of the medium), and the local expansion acts as dipolar forces parallel to the surface. A unidimension analysis lead to a local displacement $u_z$ along $z$ \cite{scruby1990laser}:
\begin{equation}
u_z =
\frac{3 \frac{(3 \lambda + 2
\mu}{\lambda \mu)}{(\lambda +
2\mu} 2\mu)} \frac{\alpha
\E}{\rho E}{\rho C S}
\label{eq:deplUnidim}
\end{equation}
where $\lambda$, $\mu$ are respectively the first and second Lamé's coefficient and $\alpha$ is the thermal dilatation coefficient. In a biological soft tissues, $\mu \gg \lambda$, so that \ref{eq:deplUnidim} becomes:
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