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The problem of the size dependence of physical properties is one of the most intriguing when we transit to the nano-level. Experiments have shown that this effect is characteristic of the elastic modulus of many polymeric nanofibers obtained by electrospinning. Existing explanations of this effect did not offer a general understanding of the physical nature of this phenomenon. In this study, we propose a universal model of this phenomenon. We consider the structure of fibers within the framework of the core-shell model, in which the shell is approximated by a thin elastic surface. The analysis of deformation is based on the fundamental laws of the mechanics of deformation of twisted thin shells and, unlike the theories proposed earlier, does not require any additional artificial arguments. This approach made it possible to obtain a simple analytical expression for the size dependence of the elastic modulus, which represents it as the sum of the bulk modulus of the core and two additional moduli proportional to D-1 and D-3, respectively. The resulting model corresponds to all available (from published sources) experimental data, related to polymer of very different chemical structure, and therefore can be considered as universal. [ABSTRACT FROM AUTHOR]