Pol Grasland-Mongrain edited Simu disp maps.tex  over 8 years ago

Commit id: dbe56ae34d88d8ce1c863057404d99906a7ef16a

deletions | additions      

       

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 of  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 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}