## 2 Materials and Methods
### Material Laws Subjected to Validation  
In this paper, two forms of the strain energy functions are used to describe the mechanical response of the arteries: the Fung proposal (for example, [31; 32]) and the Holzapfel-Gasser-Ogden model (see [33; 34]). Both are implemented in Abaqus 2019 [35].  
The Fung strain energy potential is defined, assuming that the material is incompressible, in the following form:  
\[W_{Fung}=\frac{1}{2}c\Big{(}e^{Q}-1\Big{)} \tag{1}\]  
where \(c\) is a material parameter and \(Q\) is defined as follows:  
\[Q=\overline{\epsilon}^{G}\cdot\mathbf{B}\overline{\epsilon}^{G}=\overline{ \epsilon}_{ij}^{G}b_{ijkl}\overline{\epsilon}_{kl}^{G} \tag{2}\]where \(\mathbf{B}\Leftrightarrow[[b_{ijkl}]]\) is a dimensionless symmetric fourth-order tensor of anisotropic material constants (9 independent values for the orthotropic case) and formally in a general case \(\overline{\epsilon}^{\mathrm{G}}=\frac{1}{2}(\overline{\mathbf{C}}-\mathbf{I}) \Leftrightarrow[\overline{\epsilon}_{ij}^{\mathrm{G}}]\) is the modified Green strain tensor, \(\overline{\mathbf{C}}=J^{-\frac{2}{3}}\mathbf{C}\) is the distortional part of the right Cauchy-Green strain, \(\mathbf{C}=\)F\({}^{\mathrm{T}}\mathbf{F}\) is the right Cauchy-Green strain tensor, \(\mathbf{F}=(J^{\frac{1}{3}}\mathbf{I})\overline{\mathbf{F}}\) is the deformation gradient (resulting from multiplicative decomposition of \(\mathbf{F}\) into spherical (dilatational) \(J^{\frac{1}{3}}\mathbf{I}\) and unimodular (distortional) parts \(\overline{\mathbf{F}}\)), \(J=\det\mathbf{F}\) is the volume change (\(J=1\) in this particular case), and \(\mathbf{I}\) is the identity tensor.  
For the Holzapfel-Gasser-Ogden model (herein referred to as the Holzapfel law), the strain energy potential, for an incompressible material, is formulated as the following:  
\[W_{\mathrm{HGO}}=C_{10}\big{(}\overline{I}_{1}-3\big{)}+\frac{k_{1}}{2k_{2}} \sum_{\alpha=1}^{N}\biggl{(}e^{k_{2}(\overline{\epsilon}_{\alpha})^{2}}-1 \biggr{)} \tag{3}\]  
with the strain-like quantity being the following:  
\[\overline{E}_{\alpha}\overset{def}{=}\kappa\big{(}\overline{I}_{1}-3\big{)}+ (1-3\kappa)\Big{(}\overline{I}_{4(\alpha)}-1\Big{)} \tag{4}\]  
where \(C_{10}\), \(k_{1}\), and \(k_{2}\) are material parameters; \(N\) is the number of fiber families (\(N=2\) here); and \(\kappa\) is a factor describing the fibers' distribution randomness (fibers are perfectly aligned for \(\kappa=0\), while the material becomes isotropic and the fibers are randomly distributed for \(\kappa=0.333\)). From the formal point of view and in a general case, \(\overline{I}_{1}=\overline{\lambda}_{1}^{2}+\overline{\lambda}_{2}^{2}+ \overline{\lambda}_{3}^{2}\) is the first deviatoric strain invariant, \(\overline{\lambda}_{i}^{2}=J^{-\frac{2}{3}}\lambda_{i}\) are the deviatoric stretches (in this particular case, \(J=1\)), \(\lambda_{i}\) are the principal stretches, and \(\overline{I}_{4(\alpha\beta)}=\mathbf{a}_{\alpha}\cdot\overline{\mathbf{C}} \mathbf{a}_{\beta}=a_{i}^{\alpha}\overline{\mathbf{C}}_{\mathrm{ij}}a_{j}^{\beta}\), \(\alpha=1,\ldots,N\), \(\beta=1,\ldots,\alpha\) is another invariant representing the fiber orientation (pseudo-invariant of \(\overline{\mathbf{C}}\), i.e., the distortional part of the right Cauchy-Green strain and \(\mathbf{a}_{\alpha}\), and \(\alpha=1,\ldots,N\) is the set of unit vectors defining the directions of the fibers in the reference configuration). The operator \(\langle\cdot\rangle\) stands for the Macauley bracket and is defined as \(\langle x\rangle=\frac{1}{2}(|x|+x)\).