# Non-Classical Model of Dynamic Behavior of Concrete
## 1 Introduction
Theoretical investigations are presented in a paper by [PERSON] and [PERSON] [28], in which the general structure of constitutive relations and failure criterion for concrete are described in the form of representation of tensor functions. The most complete and useful for practical application is the model of dynamic deformation of concrete presented by [PERSON] [6]. This model describes the elastic-viscoplastic-plastic-brittle-material softening features of concrete and it constitutes the specific application of [PERSON]'s elastic-viscoplasticity theory ([PERSON] [29]). Investigations in the field of dynamic modeling of concrete behavior are the subject of many scientific considerations. Computational analysis of the influence of boundary conditions on the behavior of concrete under dynamic load, described using well-known constitutive models of material, was presented by [PERSON] and [PERSON] [30]. The 3D damage model for concrete under dynamic load that includes strain rate effects and confinement effects was presented in [PERSON] et al. [31]. The model of concrete describing the dynamic failure of material under multiaxial loading was presented in [PERSON] et al. [32]. The nonlinear dynamic multiaxial strength criterion for concrete was presented in [PERSON] et al. [33]. The criterion was obtained by transforming the static multiaxial strength criterion to a dynamic criterion by building relationships between the material parameters of the static criterion and strain rate. A new material model for concrete under intense dynamic loading was presented by [PERSON] et al. [34]. This model is implemented into the commercial finite element code. Modeling of specific properties of concrete under the dynamic loads such as fragmentation of material was presented in [PERSON] and [PERSON] [35] or the fracture of material which was presented by [PERSON] et al. [36] and [PERSON] et al. [37]. The papers concerning the modeling of dynamic behavior of concrete under uniaxial compression form a separate group of papers. A paper by [PERSON] et al. [15] presented a model which described the nonlinear deformation up to attaining the dynamic strength and linear material softening. In turn, [PERSON] [16] presented the approximation of the increasing path of a dynamic stress-strain diagram in the bisectional form consisting of linear and power curves. On the other hand, in papers by [PERSON] and [PERSON] [38; 39], the nonstandard three-sectional model of dynamic deformation of concrete under uniaxial compression was presented. Applying the conclusions from static multiaxial tests results and dynamic tests results for uniaxial compression, the dynamic model for concrete in case of complex stress states is proposed in the paper. The model can be characterized as the elastic-plastic modified in the non-classical way by introducing the dynamic strength criterion by [PERSON] [40], for the purpose of the initial dynamic yield surface determination. The novelty of the proposed model is the connection of two different stages of the deformation process. Namely, process of achieving the dynamic strength of concrete, and quasi - static incremental elastic - plastic process with the initial condition at the level of determined dynamic strength. In the description of the elastic - plastic process, the model shows some similarity to the concrete plastic damage model (see: [PERSON] et al. [41], [PERSON] [42]). In the proposed model, the adopted evolution law for the yield surface in the range of material softening can be used to determine the degradation / softening parameter similar to the scalar damage parameter. This fact was used in the description of the degradation of the concrete deformation modulus. Because the comparative analysis with previously published experimental results and theoretical models showed that the proposed model well approximates the basic dynamic properties of concrete, so it can be useful in numerical analysis to evaluate the dynamic load capacity of reinforced concrete structures.