## Appendix B  
### Formulas to Estimate Equivalent Properties  
#### b.1.1 Stress-Strain Matrix  
The presented formulas correspond to the stress-strain matrix according to the classical lamination theory. \[\left[\alpha_{ij}\right]=\left[ \begin{array}{cccccc}\overline{Q}_{11}&\overline{Q}_ {12}&\overline{Q}_{13}&0&0&0\\ \overline{Q}_{12}&\overline{Q}_{22}&\overline{Q}_{23}&0&0&0\\ \overline{Q}_{13}&\overline{Q}_{23}&\overline{Q}_{33}&0&0&0\\ 0&0&0&\overline{Q}_{44}&0&0\\ 0&0&0&0&\overline{Q}_{55}&0\\ 0&0&0&0&0&\overline{Q}_{66}\end{array} \right]\left[ \begin{array}{c}\varepsilon _{1}\\ \varepsilon_{2}\\ \varepsilon_{3}\\ 2\cdot\varepsilon_{23}\\ 2\cdot\varepsilon_{31}\\ 2\cdot\varepsilon_{12}\end{array} \right] \tag{11}\]  
\[A_{ij}=\sum_{k=1}^{N}\left(\overline{Q}_{ij}\right)_{k}\cdot h_{k},\quad i, \ j\leq 3\ \text{and}\ i,j=6, \tag{12}\]  
\[A_{ij}=\sum_{k=1}^{N}\frac{h_{k}}{\left(\overline{Q}_{ij}\right)_{k}},\quad i,\ j=4,\ 5. \tag{13}\]  
Parameters \(\overline{Q}_{ij}\) are defined on [PERSON] [38]. Properties of orthotropic laminates are defined by [PERSON] [40]: generalized formulas. \[E_{x}=\frac{A_{11}\cdot A_{22}-A_{12}{}^{2}}{h\cdot A_{22}},\qquad E_{y}= \frac{A_{11}\cdot A_{22}-A_{12}{}^{2}}{h\cdot A_{11}},\qquad E_{z}=\frac{A_{1 1}\cdot A_{33}-A_{13}{}^{2}}{h\cdot A_{11}} \tag{14}\]  
\[G_{xy}=\frac{A_{66}}{h},\qquad G_{xz}=\frac{h}{A_{55}}{}^{(*)},\qquad G_{yz}= \frac{h}{A_{44}}{}^{(*)} \tag{15}\]  
\[\mu_{xy}=\frac{A_{12}}{A_{22}},\qquad\mu_{xz}=\frac{A_{13}}{A_{33}},\qquad\mu _{yz}=\frac{A_{23}}{A_{33}} \tag{16}\]  
(*) Modified as following [41]  
Appendix B.1.2. Formulas to Estimate Properties of Fiber in the Transverse Direction  
The formulas for estimating the modulus of elasticity z-direction, shear modulus, and Poisson's coefficient in the xz and yz planes for an individual ply are proposed by [PERSON] [42]:  
\[E_{z}{}^{i-p}=2\left[1-\mu_{f}+\left(\mu_{f}-\mu_{m}\right)V_{m}\right]\left[ \left(1-C\right)^{\frac{K_{r}\cdot\left(2K_{m}+G_{m}\right)-G_{m}\cdot V_{m}} {\left(2K_{m}+G_{m}\right)+\left(K_{f}-K_{m}\right)\cdot V_{m}}}\right.+C \frac{K_{r}\cdot\left(2K_{m}+G_{f}\right)+G_{r}\cdot\left(K_{m}-K_{f}\right) \cdot V_{m}}{\left(2K_{m}+G_{f}\right)-2\left(K_{m}-K_{f}\right)\cdot V_{m}}\right] \tag{17}\]  
\[G_{xz}{}^{i-p}=(1-C)\cdot G_{m}\frac{2G_{f}-\left(G_{f}-G_{m}\right)V_{m}}{2G _{m}+\left(G_{f}-G_{m}\right)V_{m}}+C\cdot G_{f}\frac{\left(G_{f}+G_{m}\right) -\left(G_{f}-G_{m}\right)V_{m}}{\left(G_{f}+G_{m}\right)+\left(G_{f}-G_{m} \right)V_{m}}, \tag{18}\]  
\[\mu_{xz}{}^{i-p}=(1-C)\frac{K_{r}\cdot\mu_{f}\cdot\left(2K_{m}+G_{m}\right) \cdot V_{f}+K_{m}\cdot\mu_{m}\left(2K_{f}+G_{m}\right)\cdot V_{m}}{K_{f}\cdot \left(2K_{m}+G_{m}\right)-G_{m}\cdot\left(K_{f}-K_{m}\right)\cdot V_{m}}+C \cdot\frac{K_{m}\cdot\mu_{m}\left(2K_{f}+G_{f}\right)\cdot V_{m}+K_{f}\cdot \mu_{f}\left(2K_{m}+G_{f}\right)\cdot V_{f}}{K_{f}\cdot\left(2K_{m}+G_{f} \right)+G_{f}\cdot\left(K_{m}-K_{f}\right)\cdot V_{m}}, \tag{19}\]  
Shear modulus and Poisson's coefficient in the yz plane are equal to those of de xz plane. where:  
\[K_{f}=\frac{E_{f}}{2\left(1-\mu_{f}\right)},\qquad K_{m}=\frac{E_{m}}{2(1-\mu _{m})}, \tag{20a}\]  
\[G_{f}=\frac{E_{f}}{2\left(1+\mu_{f}\right)},\qquad G_{m}=\frac{E_{m}}{2(1+\mu _{m})}. \tag{20b}\]  
The contiguity factor \(C\) is defined by [PERSON] [43], as:  
\[A_{ij}=\sum_{k=1}^{N}\frac{h_{k}}{\left(\overline{Q}_{ij}\right)_{k}},\quad i,\ j=4,\ 5. \tag{13}\]0  
The volume fraction \(V_{f}\) of the fiber is determined from [39]:  
\[A_{ij}=\sum_{k=1}^{N}\frac{h_{k}}{\left(\overline{Q}_{ij}\right)_{k}},\quad i,\ j=4,\ 5. \tag{13}\]1Appendix B.1.3. Formulas to Estimate Equivalent Isotropic Properties from Orthotropic Properties  
[PERSON] [44] proposes formulas to estimate equivalent isotropic properties based on the orthotropic properties defined by Equations (A4)-(A6).