PSI - Issue 59

Olena Romashko-Maistruk et al. / Procedia Structural Integrity 59 (2024) 352–359 O. Romashko-Maistruk and V. Romashko / Structural Integrity Procedia 00 (2023) 000 – 000

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3

Nomenclature  stress  strain u

specific potential energy

strain rate

έ

dynamic increase factor

DIF

2. Literature review The vast majority of concrete and reinforced concrete elements and structures studies under dynamic loads have always been directly or indirectly related to the dynamic increase factor (DIF). All types of dependencies offered today can be divided into three groups based on its definition. The first group should include dependencies according to which the DIF is determined by the dynamic load  duration (Grigoriev (2017)). Under such circumstances, it is practically impossible to take into account the any factors or effects influence on the value of the dynamic increase factor of concrete, as well as on its other characteristics. The second group consists of functions where the DIF is calculated based on the stress rate d dt /     (CEB FIP (1991), Fujikake et al. (1998), fib (2012)). However, it is extremely difficult to control this parameter in experimental studies. And in this case, there is no question of taking into account the influence of any factors or effects on the value of the concrete dynamic increase factor. Dependencies of the third group, represented mainly by power or logarithmic functions, are the most common (Dilger et al. (1984), Malvern et al. (1985), Tedesco and Ross (1998), Grote et al. (2001), Long et al. (2016)). In them, the dynamic increase factor of concrete is associated with the concrete strain rate d dt /     , and the influence of inertial effects on the dynamic increase factor of concrete - with the concrete strain acceleration d dt /      (Lee et al. (2017), Sun et al. (2022)). However, all the dependencies of this group, as well as the functions of the two previous groups, are purely empirical. Therefore, their use in generalized models of concrete deformation in concrete and reinforced concrete elements and structures remains quite problematic. Considering the above, it can be stated that the search for analytically justified dependencies of the dynamic increase factor of concrete will continue to be one of the most important tasks in the reinforced concrete theory. 3. Problem statement and solution method These studies are aimed at developing the foundations of the general model of concrete deformation in reinforced concrete elements and structures under the action of dynamic loads. At the same time, obtaining an analytical dependence of the compressed concrete dynamic increase factor should be considered one of the key tasks. It is the theoretically justified function ( )   f DIF  that will allow simulating the compressed concrete stress-strain diagram under any intensity the action of dynamic loads. The present research is based on the physical and mathematical modeling of the concrete and reinforced concrete elements deformation processes in general (Romashko (2016)) and the law of conservation of the potential energy of materials deformation under different modes of their loading, in particular. 4. Results and discussions Usually, the potential energy of material deformation is taken as the energy accumulated in the reference sample during its elastic deformation. This energy is equal to the work performed by external forces on displacements caused by the mentioned deformation of the material of the specified sample. In other words, the work performed by the external load is transformed into the potential energy of reference concrete sample deformation. It is known that