## 4 Results and Discussion
### Dynamic Tensile Testing
Upon stretching, the fibres progressively aligned with the loading direction, increasing the tangent stiffness and the wave speed of the material. The load transference was the result of a complex wave propagation phenomenon between the individual entangled fibres that could not be analysed by conventional one-dimensional wave propagation theory. The stochastic fibre network exhibited an irregular wave front due to the multiple fibre loops, and it evolved with the microstructure, increasing the apparent wave speed when aligning the fibres with the loading direction. For instance, previous authors reported an approximately linear increase in the wave speed of needle-punched nonwoven fabrics from 600 m/s in as-received condition up to 4000 m/s after 25% of deformation [27]. Additionally, the magnitude of the tensile wave decreased with the distance to the input interface due to two different sources of mechanical dissipation: (i) the frictional nature of the deformation micromechanisms and (ii) the partial wave reflection at the entanglement points. As a result of the variable stiffness and wave speed with the applied deformation, heterogeneous strain gradients developed during the dynamic testing. The wave propagation sequence is analysed in Figure 11. The tensile pulse first propagated into the specimen with velocity \(c_{0}\); see Figure 11a. The stress magnitude progressively decreased with the distance from the input bar due to the internal dissipation of the material. Afterwards, the tensile pulse reached the output interface while faster waves with a higher stress magnitude appeared at the input interface as a result of the increment of stiffness of the material with the deformation (\(c_{1}>c_{0}\)); see Figure 11b. Once the two waves (the transmitted and the reflected) travelling at different velocities arrived at the same material point, they created a macromechanical interface with an impedance mismatch at both sides due to the variation of stiffness with the evolution of the fibre alignment, preventing the propagation of larger strain waves into the left side of the specimen; see Figure 11c. The reflections were repeated during the experiment with waves of higher velocity (\(c_{2}>c_{1}\)). The result of this iterative process induced a strong strain gradient as shown in Figure 10a, with a dramatic increment of deformation nearby the input bar. The strain gradients are conventional in Split Hopkinson Bar experiments of soft materials such as gelatin or animal tissue, where the wave propagation velocity is relatively low and the duration of the pulse is not long enough to ensure dynamic force equilibrium between bars [38; 41]. The non-homogeneous deformation also occurs in the dynamic testing of non-linear elasto-plastic materials. For instance, it has been observed in metallic or epoxy foams subjected to impact [49; 50; 51; 52]. Foams usually present an initial linear elastic response followed by a plastic plateau of lower stiffness and therefore, two different waves are generated upon impact: a fast elastic precursor and a slower plastic shock front that induces a permanent deformation of the shocked region. The output forces were analysed to determine the influence of the high strain rates in the mechanical response of the fabric. Figure 12 plots the output stress monitored by the strain gauge vs. the mid-line local longitudinal strains registered by DIC at the input and output interfaces. Although the lack of a constant strain over the specimen hindered the acquisition of a conventional stress-strain constitutive equation, this methodology allows to visualise the variation in strain over the specimen mid-line at each stress level and provides the upper and lower bounds for potential high-rate stress-strain relationships. These curves are compared against the quasi-static stress-strain constitutive relationship.