## 2 Methods for Plotting Failure Envelope (MPFE)  
Utilizing the anisotropic plasticity potential, which is dependent on shear stresses and stresses perpendicular to the reinforcement direction, a unified steppe-type deformation curve was constructed. The degree parameter of this curve is employed to calculate the anisotropy of the plastic properties of the unidirectional material. Certain studies have made attempts to adapt this approach to depict the rheological properties of unidirectional composites. In our view, the mechanical behavior patterns of unidirectional composites, particularly those of carbon fiber-reinforced plastics, are more complex. However, they can be described by determining relations of a more general type, which necessitates complex experimental studies. The emphasis on the matrix is entirely justified, as it not only ensures material and structural cohesion but also contributes to the material and structural elements' crack resistance. Given that the properties of the polymer matrix and its adhesion to the fiber play significant roles when loaded at various angles to the reinforcement direction, the existence of the rheological properties of the layer is evident. This underscores the necessity for the application of defining relations of viscoelasticity and hereditary media mechanics. When formulating approaches based on viscoelasticity theory relations or hereditary mechanics, the research problem can be simplified to the construction of several interrelated functions. These include characteristics associated with energy absorption, which can be linked to both reversible deformation processes and irreversible processes, such as cracking in the matrix and delamination at the interface of the components. Numerous studies have explored the regularities of rheological behavior under different loading regimes, such as creep. Despite the seeming simplicity, there are challenges encountered in processing experimental data at the initial stage of load application. Based on the generalization of the criterion in the tensor-polynomial formulation [37]\(F_{i}\sigma_{i}+F_{ij}\sigma_{i}\sigma_{j}+F_{ijk}\sigma_{i}\sigma_{j}\sigma_{k }+\cdots=1\), \(i\), \(j\), \(k\),\(=1\), \(2\),..., \(6\), the proposed mathematical formula of MPFE is stimulated by a special case of this formulation, in which a UD layer is loaded the stress \(\sigma_{x}\) with \(F_{i}=0\); \(F_{11}=0\); \(F_{22}=\frac{1}{m^{2}}\); \(F_{66}=\frac{1}{m^{2}}\); \(F_{266}=\frac{k}{m^{2}}\), where \(m\), \(n\), \(k\) are coefficients of the proposed mathematical formula of MPFE. Therefore, the failure envelope can be described by the following equation in coordinates \((\sigma_{2},\tau_{6})\):  
\[\frac{\sigma_{2}^{2}}{m^{2}}+\frac{\tau_{6}^{2}}{n^{2}}(1+k\sigma_{2})=1, \tag{4}\]  
where \(\sigma_{2}\)--normal stress in the perpendicular direction to the fiber reinforcement; \(\tau_{6}\)--in-plane shear stress; \(m=\frac{\sigma_{2}^{+}-\sigma_{2}^{-}}{2}\); and \(k\) and \(n\)--coefficients obtained from experimental data. We take coefficients \(m\), \(n\), \(k\) as symbols to simplify Formula (4); thus, these coefficients have no physical meaning but are mathematical values. \(\sigma_{2}^{+}\), \(\sigma_{2}^{-}\) are the tensile strength value (\(\sigma_{2}^{+}>0\)) and compression strength value (\(\sigma_{2}^{-}<0\)), respectively, in the direction transverse to the reinforcement. To account for the influence of strength anisotropy in the direction transverse to the reinforcement, the ordinate axis is shifted by \(\alpha=\frac{\sigma_{2}^{+}+\sigma_{2}^{-}}{2}\) (as shown in Figure 3). Then, Equation (4) can be replaced by following expression:  
\[\frac{(\sigma_{2}-\alpha)^{2}}{m^{2}}+\frac{\tau_{6}^{2}}{n^{2}}[1+k(\sigma_{ 2}-\alpha)]=1, \tag{5}\]  
To plot the failure envelope of the material, it is necessary to find the values of the coefficients \(n\) and \(k\).