## 5 Analysis of Results and Discussion
### Energy-Penetration Behavior  
Dynamic loading on structures is accompanied by a large transfer of mechanical energy. To numerically explore the behavior of structural elements under impact loading, consideration of the energy balance should be the first step [28]. In the FEA, the impactor and the concrete element were presented as a single mechanical system. Before impact, the drop weight only had kinetic energy, while during impact, the drop weight slowed down significantly (lost a substantial part of its kinetic energy) due to the energy dissipation capability of the concrete element. Figure 15 presents the experimental and numerical applied energy-penetration depth curves for the ECC specimens at different drop levels. It can be observed that the CDP and DP models could closely estimate the experimental behavior of the ECC specimens under impact loading. Table 5 reports the experimental and numerical results for all tested specimens. Although the DP model exhibited good estimation of the applied energy at the first impact, the CDP model generally displayed better performance in simulating experimental results at higher impact levels. Figure 16 displays the strain energy magnitude propagated through the ECC specimens due to impact loading at different time intervals along with that remaining in the specimen after impact. It can be observed that the propagated energy kept increasing through the specimen during the impact process, while it was partially reversed (dissipated) upon removal of the load. The amount of applied energy which remained or dissipated in the system depended mainly on the energy dissipation capability of the tested material. Figure 17 illustrates the total energy dissipated through all impact levels for the various ECC specimens. It can be observed that the numerical and experimental values of dissipated energies were in good agreement. During experimental testing, cracks were usually captured when their width was sufficiently developed, while in numerical simulations, they could be detected at earlier stages. This could result in estimating numerical dissipated energies that were lower than their corresponding experimental values. Also, it can be observed that the total energy dissipated through the ECC specimens using the CDP model was in better agreement with the experimental results compared to that of the DP model. For instance, the total energy dissipated through the ECC2-0, ECC2-0.5, ECC2-1, and ECC2-1.5 specimens using the CDP model was 24.4%, 17.3%, 18.8%, and 21.9% lower than that of the experimental results, respectively. However, using the DP model, the total energy dissipated was 58.0%, 61.5%, 61.1%, and 56.6% lower than the corresponding experimental results, respectively. Similarly, the numerically estimated penetration depth of the different ECC specimens under multiple impacts was in good agreement with corresponding experimental observation, as shown in Table 5. Figure 18 displays the accumulated penetration depth measured through the different ECC specimens due to multiple impacts. Furthermore, Figures 19 and 20 show the total numerically estimated penetration depth using the CDP and DP models, respectively. It can be observed that the CDP model was more accurate than the DP model in predicting the penetration depth upon multiple impacts. For instance, the total penetration depth determined by the CDP model for the ECC2-0, ECC2-0.5, ECC2-1, and ECC2-1.5 specimens was 1.1%, 7.2%, 12.1%, and 3.7% higher than the experimental results, respectively. However, the total penetration depth estimated using the DP model was 25.1%, 21.2%, 18.7%, and 12.6% higher than the experimental results, respectively.