## 3 Results and Discussion
### Analytical Results
#### 3.1.2 Influence of Elastic Parameters on Radial Strain Distributions  
For plane inclinations different from \(\beta=0^{\circ}\), the resulting radial strain curves are influenced by the ratios \(E/E^{\prime}\) and \(\
u/\
u^{\prime}\). Additionally, the shear modulus \(G^{\prime}\) influences the cases with \(\beta=45^{\circ}\). Figure 10 displays the radial strain distributions in dependency of ratios \(E/E^{\prime}\) and \(\
u/\
u^{\prime}\) for samples with plane inclinations \(\beta\) of \(45^{\circ}\) and \(90^{\circ}\). The curves are depicted for a constant value of \(G^{\prime}\) selected as \(G^{\prime}_{sv,Ent=2}\) computed for a ratio \(E/E^{\prime}=2\) using Equation (5). It can be seen that increasing ratios \(\
u/\
u^{\prime}\), corresponding to an increase in the Poisson's ratio \(\
u\), result in increased radial strains in the vicinity of the \(y\)-axis with vanishing influence toward the \(x\)-axis. This statement holds independently of the investigated ratios \(E/E^{\prime}\) and isotropy plane inclinations of \(\beta=45^{\circ}\) and \(90^{\circ}\). The radial strains on the \(x\)-axis, which corresponds to the samples' symmetry plane, remain unaffected by changing values of \(\
u\). At constant ratio \(E/E^{\prime}\) with fixed values for the Young's moduli and \(\beta=45^{\circ}\), the only two parameters influencing the radial strains along the \(x\)-axis are Poisson's ratio \(\
u^{\prime}\) and the transverse shear modulus \(G^{\prime}\). For \(\beta=90^{\circ}\), the shear modulus \(G^{\prime}\) does not affect the resulting strains. The radial strains along the \(x\)-axis are exclusively determined by the parameters \(\
u^{\prime}\) and \(E^{\prime}\). As both parameter values are fixed for the curves shown in Figure 10, the values for the radial strains along the \(x\)-axis from curves with constant ratio \(E/E^{\prime}\) do not differ. For cases with \(\beta=45^{\circ}\), increasing values for the [PERSON]'s modulus \(E\) for otherwise constant elastic parameters leads to a reduction in the radial strains in the vicinity of the \(y\)-axis. The strains along and close to the \(x\)-axis increase. For samples with an isotropy plane inclination of \(\beta=90^{\circ}\), only the strains toward the \(y\)-axis direction are affected by varying values for the Young's modulus \(E\). Figure 9: Analytical strain distributions for samples with isotropy plane inclination \(\beta=0^{\circ}\) plotted in a range of \(\theta=0^{\circ}\) to \(360^{\circ}\) for various ratios \(\
u/\
u^{\prime}\): (a) vertical strains \(\epsilon_{z}\) and (b) radial strains \(\epsilon_{r}\). Obviously, no dependency on ratios \(E/E^{\prime}\), \(\
u/\
u^{\prime}\) or the shear modulus \(G^{\prime}\) is given. It holds that, for samples with isotropy plane inclinations of \(\beta=90^{\circ}\), uniform radial strain distributions are obtained in the case of equal ratios \(E/E^{\prime}\) and \(\
u/\
u^{\prime}\). For samples with \(\beta=45^{\circ}\) and \(E/E^{\prime}=\
u/\
u^{\prime}\), the uniformity of radial strains is only guaranteed when, additionally, the shear modulus is equal to \(G^{\prime}_{\text{s}\text{s}}\) derived from the approximation provided by Equation (5). In Figure 10, this is only the case for the curve with \(E/E^{\prime}=\
u/\
u^{\prime}=2.0\), since all curves from this figure result from computations with a constant shear modulus \(G^{\prime}=G^{\prime}_{\text{s}\text{s},E\text{r}at=2}\) evaluated for a ratio \(E/E^{\prime}\) of 2.0. Under this assumption, for the shear modulus \(G^{\prime}\), uniform radial strains at any other ratio \(E/E^{\prime}\) are only satisfied for specific values \(K\) of the ratio \(\
u/\
u^{\prime}\) acc. to Equation (10). An example is given by the curve in Figure 10 with \(E/E^{\prime}=1.5\), \(\
u/\
u^{\prime}=0.667\) and \(\beta=45^{\circ}\).