## 1 Introduction
It was demonstrated that the Puck criterion provides accurate strength predictions for both quasi-static and dynamic loading when compressing UD CFRP perpendicular to the reinforcement direction. NU-Daniel failure theory [7; 8; 9; 10] successfully demonstrated excellent prediction capability and agreement with experimental data. Notably, the failure envelopes obtained using this theory are characterized by three equations corresponding to the predominant failure type at a specific location--tension, shear, and compression. The equation of three sub-criteria for inter-fiber and interlaminar failure in NU-Daniel criteria are composed of following formulations [7]:  
Compression-dominated failure:  
\[\left(\frac{\sigma_{2}}{F_{2c}}\right)^{2}+\left(\frac{E_{2}}{G_{12}}\right)^{ 2}\left(\frac{\tau_{6}}{F_{2c}}\right)^{2}=1 \tag{1}\]  
Shear-dominated failure:  
\[\left(\frac{\tau_{6}}{F_{6}}\right)^{2}+\left(\frac{2G_{12}}{E_{2}}\right)^{ 2}\frac{\sigma_{2}}{F_{6}}=1 \tag{2}\]  
Tension-dominated failure:  
\[\frac{\sigma_{2}}{F_{2t}}+\left(\frac{E_{2}}{2G_{12}}\right)^{2}+\left(\frac{ \tau_{6}}{F_{2t}}\right)^{2}=1 \tag{3}\]  
where \(F_{2c}\)--transverse compressive strength; \(F_{2t}\)--transverse tensile strength; \(F_{6}\)--shear strength; \(F_{2}\)--transverse modulus; \(G_{12}\)--shear modulus; \(\sigma_{2}\)--normal stress in the perpendicular direction to the fiber reinforcement; \(\tau_{6}\)--in-plane shear stress. Figure 1 is illustrated for a better understanding of these mechanical properties of UD fiber-reinforced polymers. The NU-Daniel criterion satisfied many UD composite materials better compared with other criteria, as shown in Figure 2, including Tsai-Wu, Tsai-Hill, Hashin-Rotem, Sun, Max. Stress, etc. It is important to highlight that the NU-Daniel failure theory exhibits strong potential in accurately describing the behavior of UD CFRP and predicting its strength. However, using three different equations to describe the failure envelopes for different strain rate cases makes the prediction and calculation methods appear complicated. The latest works on failure criteria [18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28] focused on empirical numerical constitutive equations to predict mechanical behavior and perform computational analysis. In [18], the main objective of the study was to analyze the mechanical behaviors of a UD fiber-reinforced polymer composite subjected to transverse tension. Nonlinear deformation and damage in the matrix and debonding in the interface were considered to investigate the ultimate strength, failure strain, damage initiation, and evolution process. [PERSON] et al. [19] proposed a numerical constitutive equation to predict the regularities of UD fiber-reinforced epoxy sheet molding compounds, and a uniaxial tensile experiment was implemented to study the progressive damage criterion. There are also many experimental and numerical methods [20; 21; 22; 23; 24] devoted to investigating the failure mechanical behaviors of UD fiber-reinforced polymer composites. [PERSON] et al. [25] proposed a new set of homogenized failure  
Figure 1: An explanation of mechanical properties of UD fiber-reinforced polymers. Figure 2: Comparison of failure envelopes using different failure criteria and experimental results for UD AS4/3501-6 CFRP under quasi-static transverse normal and shear stress (Reprinted with permission from Ref. [7]. 2011, copyright owner’s [PERSON].) [7]. criteria of \(\sigma_{22}-\tau_{12}\) and \(\sigma_{22}-\tau_{23}\) based on computational micromechanics representative volume element (RVE) analysis, in which the mechanical properties of the constituents can be obtained from the experiments. RVE modeling offers a novel approach for a better understanding of the deformation and fracture mechanisms. They have identified three dominant failure mechanisms or modes from the computational RVE model under multi-axial loading conditions, which are tension-, shear-, and compression-dominated failure modes.