## 2 Materials and Methods
### Computational Model  
The constitutive model is based on the damage evolution rule from a tensile failure surface and the definition of the scalar damage parameter, according to four material parameters. These are defined from the different properties determined in a tension  
Figure 4: Dimension and shape of samples. (a) Tensile test and (b) impact test. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Sample** & **Fiber [\%]** & **Bentonite [\%]** \\ \hline PoS & - & - \\ PoH15 & 15 & - \\ PoH20 & 20 & - \\ PoH25 & 25 & - \\ PoB3 & - & 3 \\ PoB5 & - & 5 \\ PoB7 & - & 7 \\ PoB5H15 & 15 & 5 \\ PoB5H20 & 20 & 5 \\ PoB5H25 & 25 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Denomination and composition of the prepared samples. displacement test, implemented in the commercial software ABAQUS ([PERSON], 2014) by means of a subroutine with explicit VUMAT integration. A single scalar variable, \(d\), that affects all the components of the tensor equally maintaining isotropy conditions [31; 32], was proposed once the damage starts with respect to the Hashin criterion, that does not violate the first and second laws of thermodynamics [24]. The damage variable had a domain of \([0,1]\), with value \(1\) for not damaged, and value \(0\) for completely damaged. The stress tensor expressed is presented in Equation (3), where \(\sigma_{ij}\) is the stress tensor of the real space, \(\overline{\sigma}_{ij}\) the effective stress tensor or the undamaged space, \(C^{0}_{ijkl}\) the elastic constitutive tensor, \(\epsilon_{kl}\) the deformation tensor, and \(d\) the damage variable, according to [31]. The validation was obtained from the contrast with the results obtained in the experimental tests, according to the ASTM D3039 standard for the case of an element subjected to increasing axial traction. \[\sigma_{ij}=(1-d)\overline{\sigma}_{ij}=(1-d)C^{0}_{ijkl}\epsilon_{kl} \tag{3}\]  
A linear elastic model was implemented that satisfies the following stability conditions: Equilibrium condition  
\[\frac{\partial\sigma_{ij}}{\partial x_{j}}=-\rho b_{i} \tag{4}\]  
Equilibrium condition on the boundary  
\[\sigma\cdot n=t \tag{5}\]  
Infinitesimal strain condition  
\[\varepsilon_{ij}=\frac{1}{2}\left(\frac{\partial u_{i}}{\partial x_{j}}+\frac {\partial u_{j}}{\partial x_{i}}\right) \tag{6}\]  
The linear relationship such as the generalized Hooke's law meets these conditions and is presented in Equation (7). \[\sigma_{ij}=C_{ijkl}\epsilon_{kl} \tag{7}\]  
The constitutive fourth order tensor, \(C_{ijkl}\), has only two independent terms, which are [PERSON]'s modulus, E and the [PERSON]'s ratio, \(\
u\), and was used only in the zone of elastic behavior as presented in Equation (8) where \(\mu\) and \(\lambda\) are the [PERSON]'s constants. \[\sigma_{ij}=\mu\varepsilon_{ij}+\lambda\epsilon_{kl}\delta_{ij} \tag{8}\]  
For the model to have physical and numerical stability, the Drucker criterion was used, while the stability condition is guaranteed if the Hessian is definitively positive [33]. \[H_{ijkl}=\mathbf{H}=det\left|\frac{\partial^{2}\Psi(\varepsilon)}{\partial \varepsilon\bigotimes\partial\varepsilon}\right|>0 \tag{9}\]  
The implemented continuous damage model begins when the discontinuity criterion is satisfied, based on a scalar function of tensor arguments that delimits the elastic domain. In this way, the main objective of this model is to reduce the properties of the stiffness matrix, in response to the loss of properties, since different studies affirm that composite materials present a subcritical damage prior to the total damage of the material. On the other hand, the criterion for the onset of damage, according to the physical nature of the model, is presented in Equation (10), which allowed evaluating the effective tension in the longitudinal direction when it is in tension (\(\overline{\sigma}_{11}>0\)), where \(X_{T}\) is the tensile strength in the direction of the fibers.