Analytical and Numerical Modeling of Composite Materials with Thin and Stiff Reinforcements
Prof. Sofia Mogilevskaya
University of Minnesota
Tuesday, October 3, 2023
Mason Building, Room 2117
Emerging generations of nanomaterials and biomaterials use ultrathin nanoplatelets or membrane sheets as reinforcements. In the talk, I will discuss the use of the theories of material surfaces for modeling such materials. The theories describe an infinite isotropic elastic medium that contains a material surface treated as either a membrane or a shell of vanishing thickness. The material surface is characterized by its own elastic stiffness as well as residual surface tension. The governing equations of the theories are reviewed and challenges associated with the theoretical analysis and numerical solutions of resulting non-classical boundary value problems are discussed. For solving the problems, the displacements in the matrix are sought in the form of a single layer elastic potential. The potential is continuous across the surface and its density represents the jump in tractions across that surface. Exact expressions for the elastic fields in the matrix are provided in terms of integral representations. The solutions for the two-dimensional cases of multiple surfaces along straight segments or for a single circular arc will be presented and the dimensionless parameters that govern the problems will be identified. The numerical examples, that illustrate the influence of the parameters on the local elastic fields in the material, will be presented. Extension to three-dimensional problems will be discussed.
Prof. Mogilevskaya received her PhD in Engineering Mechanics from the Scotchinsky Research Institute of Mining (Russian Academy of Sciences, Moscow) in 1987. She was an Associate Professor at the Department of Mathematics of the Kuzbass State Technical University in Russia before joining the Department of Civil, Environmental, and Geo- Engineering at the University of Minnesota in 1999. She is currently a Research Professor and a Member of the Graduate Faculty. She has published over 95 archival journal papers and co-authored a chapter in the book on complex hypersingular BEM in plane elasticity problems. At the UMN, she taught a graduate course on the Boundary Element Methods and, currently, together with Prof. Steve Crouch is completing a book on that subject. In 2019, she was a Simons INI Visiting Fellow at the Isaac Newton Institute, Cambridge and, in 2022, a Visiting Fellow at the Mathematisches Forschungsinstitut Oberwolfach, Germany. In 2021, she received the University of Minnesota award for Global Engagement in recognition of outstanding contributions to global education and international programs at the University and in the field of discipline.