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

Commit id: 23501cefa0cfadbce2ff6017a6d49e9f5d35ce25

deletions | additions      

       

\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), $T_V-T_0$ = 373-293 = 80 K (water vaporization temperature minus laboratory temperature), $C$ = 4180 J.kg$^{-1}$.K$^{-1}$, $\rho$ = 1000 kg.m$^{-3}$, $E$ = 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).  This To calculate the propagation of the  displacement along Z can create shear waves. We space and time, we  modeled the ablation regime as a point force directed along Z direction with a depth of 50 $\mu$m and increasing linearly from -2.5 to 0 mm and decreasing symmetrically from 0 to 2.5 mm, to simulate an approximate Gaussian shape. mm.  Propagation as a shear wave was calculated using Green operators $G_{zz}$ \cite{aki1980quantitative}: \begin{equation}  G_{zz}(r,\theta,z,t) = \frac{\cos^2 \theta}{4\pi \rho c_p^2 r} f(t-\frac{r}{c_p}) + \frac{\sin^2 \theta}{4\pi \rho c_s^2 r} f(t-\frac{r}{c_s}) + \frac{3\cos^2 \theta-1}{4\pi \rho r^3} \int_{r/c_p}^{r/c_s}{\tau f_{NF}}  \label{eq:Gzz}