On the Modeling and Approximation of Phase Transitions in Elasticity
This talk explores the mathematical modeling of phase transitions in elasticity, drawing motivation from observed phenomena in crystalline solids and biomaterials.
Overview
A central difficulty in finite elasticity is that the physical necessity of frame invariance precludes the convexity of the strain energy function. While weaker notions such as polyconvexity and quasiconvexity allow for the existence of weak solutions, experimental evidence of multi-well energy landscapes often violates even these relaxed conditions. We will discuss the specific analytical and numerical challenges posed by non-convex, multi-well strain energy functions and highlight the limitations of current approximation methods.
Presenters
Brief Biography
Georgios Grekas is a Postdoctoral Research Fellow in the Applied PDE Group of the Applied Mathematics and Computational Science (AMCS) program, within the CEMSE Division at King Abdullah University of Science and Technology (KAUST), Saudi Arabia. He received his Ph.D. degree in Applied Mathematics from the University of Crete in 2019. Part of his Ph.D. studies took place at the University of Sussex from March 2016 to March 2018. From 2019 to 2022, he held a postdoctoral position at the Department of Aerospace Engineering and Mechanics at the University of Minnesota. He then worked as a postdoctoral researcher at the Institute of Applied and Computational Mathematics (IACM) of FORTH, Greece. He joined KAUST and the Applied PDE Group in March 2024.
Related People
Related Researchers
Georgios Grekas
- Postdoctoral Research Fellow, Applied Mathematics and Computational Science