Paulina Stempin
My research focuses on continuum mechanics in its non-local formulation and on modeling scale effect, particularly in structures of nano- and micro-scale dimensions. I develop the theoretical framework of space-Fractional Continuum Mechanics and propose new mathematical and numerical models within this theory.
This work began with my doctoral dissertation „Structural models in the framework of space-Fractional Continuum Mechanics” (supervisor: Prof. Wojciech Sumelka, Poznan University of Technology) and is now continued under the PRELUDIUM grant Mechanics of bar-and-plate structures with strong scale effects – mathematical modelling and experimental analysis, no. 2022/45/N/ST8/02421, funded by the National Science Center, Poland.
The project advances the space-Fractional Continuum Mechanics framework for non-local modeling of scale effects in nano- and micro-sized structures. It develops mathematical and numerical tools for trusses, frames, plates, and plate–beam systems, supporting accurate analysis of their behavior when size-dependent phenomena are significant.
To ensure both theoretical and practical relevance, the research combines mathematical modeling, numerical simulation, and experimental validation. The developed models account for static and dynamic responses of structures where traditional (local) continuum theories fail to describe size-dependent behavior. The results are expected to improve understanding and prediction of the mechanical performance of nano- and micro-structures and lay the foundation for design tools used in nano- and micro-scale engineering applications.