# Non-Classical Model of Dynamic Behavior of Concrete
## 3 Comparative Analysis
### Comparisons for Static Tests  
A comparison of the proposed model with the experimental stress-strain curves was carried out on the basis of the experimental results of [PERSON] et al. [1]. In Figure 5 for uniaxial compression (\(\sigma_{11}=\sigma\), \(\sigma_{22}=\sigma_{33}=0\)), theoretical results were marked with solid lines, while the experimental curves according to [1] were marked with dashed lines. In Figure 5a, the variation of stress as a function of strain \(\varepsilon_{11}\) \"forcing\" the considered stress state and as a function of transverse strains \(\varepsilon_{22}=\varepsilon_{33}\) resulting from volumetric strains \(\varepsilon_{0}=\frac{1}{3}\varepsilon_{kk}\), was presented for different \(\beta\) values in the plastic potential function (Equation (16)). Graphs of stress changes as a function of strains \(\varepsilon_{kk}\) are shown in Figure 5b. The result for \(\beta=1\) corresponds to the solution obtained for the associated flow rule \(G=F\). The variability of the presented stress-strain curves is characteristic for the introduced model. The occurrence of the linear elastic phase, the perfectly plastic flow phase in a limited range of strains, and the material softening phase is observed in Figure 5a. The change of volumetric strains in these phases is typical for brittle materials (Figure 5b). In the initial elastic phase, the volume strains increase and the material undergoes to compaction. In the perfectly plastic flow phase, the volume strains decrease. In the softening phase the material undergoes loosening as well, but in this case, with decreasing stresses. Figure 6 presents analogous results for the case of symmetrical, biaxial compression (\(\sigma_{11}=\sigma_{22}=\sigma\), \(\sigma_{33}=0\)). Figure 6a relates to stress changes \(\sigma_{11}=\sigma_{22}=\sigma\) in the function of strains \(\varepsilon_{11}=\varepsilon_{22}\) and in the function of transverse strains \(\varepsilon_{33}\) determined from the law of volume changes. Figure 6b presents graphs of stress changes \(\sigma_{11}=\sigma_{22}=\sigma\) in the function of volumetric strains \(\varepsilon_{0}=\frac{1}{3}\varepsilon_{kk}\). On the basis of presented comparisons of theoretical solutions with experimental results, it can be concluded that the graphs of probable stress changes as a function of volumetric strains and as a function of transverse strains should be consistent with the graph of stress changes as a function of strains \"forcing\" the considered stress state. Such theoretical solutions--characterized by the presence of a distinct range of material softening in all of the mentioned relationships--are obtained for the constant \(\beta\gg 1\). The solution for \(\beta=1\)--corresponding to the associated flow rule--practically does not describe changes in the volume of material and can be considered as unrealistic. However, in the literature there are no experimental results concerning the changes in volumetric strains of the concrete over the whole range of material softening, it can be assumed that the theoretical solutions obtained for interval \(\beta=\langle 9,\;\;36\rangle\) approximately describes the real behavior of the concrete. Figure 7 presents the comparison of the proposed model with the theoretical solution developed on the basis of the degradation theory, placed in the paper by [PERSON] and [PERSON] [27]. The solution concerns a plane, symmetrical stress state (\(\sigma_{11}=\sigma_{22}=\sigma,\sigma_{33}=0\)). Material data were adopted according to the cited work. The presented results were obtained for the constant \(\beta\) occurring in the plastic potential function (Equation (16)) with the values in the interval \(\beta=\langle\;18,\;27\rangle\). The general agreement of the proposed model with the solution [27] is noteworthy, although both solutions are qualitatively different. This agreement relates primarily to the points of the maximum stresses shown in the graphs \(\sigma=\sigma(\varepsilon)\).