## 3 Results
### Optimization of Thermomechanical Effect  
The effect of processing parameters (wavelength W, beam size S, laser intensity I, and exposure time T) on temperature and stress distributions was studied in the skin using Box-Behnken design optimization (Table 2). The optimal parameter levels corresponding to the minimum values for each temperature were also determined T\({}_{\text{max}}\) (\(\leq\)43 \({}^{\circ}\)C) and stress S\({}_{\text{max}}\) (\(\leq\)0.2 MPa). Table 2 shows the experiment array consisting of 30 runs according to the Box-Behnken design to evaluate the effect of the following parameters: wavelength (W), intensity (I), beam diameter expressed as beam size (S), and skin exposure time to the laser (T). On the change in each of the two responses studied (maximum temperature T\({}_{\text{max}}\) and stress S\({}_{\text{max}}\)). Table 3 shows the results of the ANOVA analysis of variance between the averages of the studied response under the influence of the four influential parameters using IBM SPSS Statistics version 26.0 (SPSS Inc., Chicago, IL, USA), clarifying the presence or absence of statistically significant differences depending on the probability value (\(p\)-value) at a confidence interval (\(\alpha\) = 0.05). The results of the analysis of variance showed that there was no statistical significance for the effect of both beam size S (\(p\) = 0.999 \(>\) 0.05) and wavelength (W) (\(p\) = 0.965 \(>\) 0.05). At temperature T\({}_{\text{max}}\), in contrast, both the beam intensity (I) and the exposure time (T) have statistical significance, with a combined contribution of the two parameters estimated at 89.6%. Figure 10a illustrates the average impact of the mentioned  
Figure 9: Distribution of model displacements in skin model layers at wavelengths 532 and 800 nm, laser intensities of 1 and 2 W/mm\({}^{2}\), and beam widths of 1 and 2 mm. parameters on (T\({}_{\rm max}\)). The figure indicates that the response remains unaffected by S and W. In contrast, the results of the analysis of variance showed that there is no statistical significance for the effect of the beam size S (\(p\) = 1.00 > 0.05) only on the stress value S\({}_{\rm max}\). In contrast, the wavelength (W), the beam intensity (I), and the exposure time (T) have statistical significance. The combined contribution of the three parameters is estimated at 71.6%. Figure 10b also shows the average effect of the mentioned parameters on (S\({}_{\rm max}\)). \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **Intensity** & **Size** & **Time** & **Wavelength (\(\lambda\))** & **Temperature** & **Stress** \\
**Run** & **I** & **S** & **T** & **W** & **T\({}_{\rm max}\)** & **S\({}_{\rm max}\)** \\  & **[W/mm\({}^{2}\)]** & **[mm]** & **[s]** & **[nm]** & **[\({}^{\circ}\)C]** & **[MPa]** \\ \hline  
5 & 30 & 800 & 42.56 & 0.57 \\ \hline \end{tabular}
\end{table} 
Table 2: The Box-Behnken design of thermomechanical optimization (parameters, levels, and responses). \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & **Source** & **DF** & **Adj SS** & **Adj MS** & **F-Value** & **\(p\)-Value** & **Contrubtion** & **R-sq** \\ \hline  & I & 2 & 4769.00 & 2384.50 & 57.24 & 0.000 & 50.1\% & \\  & S & 2 & 0.05 & 0.02 & 0.00 & 0.999 &... & \\ T\({}_{\rm max}\) & T & 2 & 3718.45 & 1859.23 & 44.63 & 0.000 & 39.5\% & \\  & W & 1 & 0.08 & 0.08 & 0.00 & 0.965 &... & \\  & Error & 22 & 916.40 & 41.65 & & & 9.7\% & \\  & Total & 29 & 9414.06 & & & & & \\ \hline  & I & 2 & 17.2383 & 8.6191 & 9.32 & 0.001 & 24.1\% & \\  & S & 2 & 0.0000 & 0.0000 & 0.00 & 1.000 &... & \\  & T & 2 & 9.1414 & 4.5707 & 4.94 & 0.017 & 12.8\% & \\ S\({}_{\rm max}\) & W & 1 & 24.9403 & 24.9403 & 26.96 & 0.000 & 34.7\% & \\  & Error & 22 & 20.3488 & 0.9249 & & & 28.3\% & \\  & Total & 29 & 71.6918 & & & & & \\ \hline \end{tabular}
\end{table} 
Table 3: Analysis of variance (ANOVA) to estimate the parameters’ effect for each response (T\({}_{\rm max}\), S\({}_{\rm max}\)) and determine \(p\)-values (at \(\alpha\) = 5%).