# Non-Classical Model of Dynamic Behavior of Concrete
## 3 Comparative Analysis
### Comparisons for Dynamic Tests
The static limit curve of Equation (1) was determined for the test data and assuming \(K=1\), \(\varphi_{t}=0.1\), \(\varphi_{cc}=1.1\). The dynamic limit curve of Equation (1) was determined for the dynamic strength coefficient \(K=\psi_{d}=1.23\) calculated according to criterion of Equation (8) with material constants from Equation (11). Comparison of the results indicates a good agreement between the proposed theoretical limit curves and the experimental results. Figure 9: Comparison of the proposed dynamic strength criterion with experimental results by [PERSON] and [PERSON] [49] for biaxial compressive–compressive loading tests. In Figure 11, comparison of the proposed dynamic strength criterion with selected experimental results conducted by [PERSON] and [PERSON] [51] for biaxial tensile-compressive loading tests, is presented. The experimental results were conducted concrete with uniaxial compressive \(f_{c}=31.2\)_MPa_ and tensile \(f_{ct}=3.826\)_MPa_ strengths. The experimental results presented in Figure 11 relate to the loading process with \(\sigma_{33}=0\) and constant values of tensile stresses \(\sigma_{22}=(0\) ; \(0.7\) ;\(1.4\) ;\(2.1\) ;\(2.8)\)_MPa_ (i.e., \(\frac{\sigma_{22}}{f_{c}}=0\) ; \(-0.022\) ;\(-0.045\) ;\(-0.067\) ;\(-0.090\)). For strain rate \(\dot{\varepsilon}=10^{-5}\)\(s^{-1}\) (set as static loading rate) axial stresses have been obtained with values of \(\frac{\sigma_{11}}{f_{c}}=1.00\) ;\(0.857\) ;\(0.679\) ; \(0.487\) ; \(0.318\). For strain rate \(\dot{\varepsilon}=10^{-2}\)\(s^{-1}\)  
Figure 11: Comparison of the proposed dynamic strength criterion with experimental results by [PERSON] and [PERSON] [51] for biaxial tensile–compressive loading tests. Figure 10: Comparison of the proposed dynamic strength criterion with experimental results by [PERSON] and [PERSON] [50] for biaxial compressive–compressive loading tests. dynamic axial stresses have been obtained with values of \(\frac{\sigma_{11}}{f_{c}}=1.128\) ; \(1.037\) ; \(0.901\) ; \(0.663\) ; \(0.398\). The static limit curve of Equation (1) was determined for the test data including \(\varphi_{t}=0.123\) and assuming \(K=1\), \(\varphi_{cc}=1.1\). The dynamic limit curve of Equation (1) was determined for the dynamic strength coefficient \(K=\psi_{d}=1.21\) calculated according to criterion of Equation (8) with material constants from Equation (11). Comparison of the results indicates that the proposed theoretical limit curves are in quite good agreement with the experimental results. The second group of dynamic tests refers to the comparison of the proposed model with experimental dynamic curves available in the literature and known theoretical models of dynamic deformation of concrete. These comparisons were performed for uniaxial compression (\(\sigma_{11}=\sigma\), \(\sigma_{22}=\sigma_{33}=0\)); the most reliable for the assessment of the dynamic load capacity of concrete. Figure 12 shows the compatibility of the proposed model in terms of strains \(\left\langle 0,\ \varepsilon_{fc}\right\rangle\) with some results of [PERSON] [10]. The experimental results obtained in dynamic and static tests, were marked with continuous and dotted lines, respectively, and the proposed idealization was marked with a discontinuous line. Noteworthy is the increasing linear range of deformation observed in the experimental dynamic curves \(\sigma-\varepsilon\) with respect to the static curves. The proposed model approximates well the experimental results for the tested range of strains. An agreement in results for the same range of strains \(\left\langle 0,\ \varepsilon_{fc}\right\rangle\) also demonstrate the comparisons presented in Figure 13, based on the work of [PERSON] and [PERSON] [18]. The disagreement of the model with experimental results in the range of material softening is influenced by the length of the strain measuring base \(\varepsilon^{(24)}\) which is equal to the length of the sample (i.e., \(24^{\prime\prime}\cong 0.60\ m\)).