Asymptotic properties of composites

Abstract

In this talk, I will start with an overview of my research to date. Then, I will address in more detail the study of the asymptotic behavior of a two-dimensional variational model within finite crystal plasticity for high-contrast bilayered composites. More precisely, we consider materials arranged into periodically alternated thin horizontal strips of an elastically rigid component and a softer one with one active slip system. The energies arising from our modeling assumptions are of integral form, featuring linear growth and non-standard differential constraints. Our asymptotic analysis is based on Gamma-convergence. A key step in this analysis is the characterization of rigidity properties of limits of admissible deformations in the space BV of functions of bounded variation. In particular, in certain cases, we prove that the two-dimensional body may split horizontally into finitely many pieces, each one of these undergoing through a globally rotated shear deformation. This allows us to identify a potential candidate for the homogenized limit energy, which we show to be a lower bound for the Gamma-limit. In the framework of non-simple materials, we present a complete Gamma-convergence result, including an explicit homogenization formula, for a regularized model with an anisotropic penalization in layer direction.

Brief Biography

Rita Ferreira is a Research Scientist at KAUST in the research group of Prof. Diogo Gomes, within the CEMSE Division. Rita received her dual Ph.D. degree in Mathematics at Carnegie Mellon University (CMU), USA, and at the New University of Lisbon (UNL), Portugal, in 2011. She was supervised by Prof. Irene Fonseca (CMU) and Prof. Luísa Mascarenhas (UNL). Before joining KAUST in 2014, Rita was a Visiting Assistant Professor at the Department of Mathematics of the Faculdade de Ciências e Tecnologia of the New University of Lisbon, Portugal, and a Postdoctoral Research Fellow at Instituto Superior Técnico of the University of Lisbon, Portugal. Rita's research activities intersect applied and pure mathematics and are driven by applications to physical and socio-economic sciences and engineering. Her domain of specialization is based on variational and asymptotic techniques to study minimization problems and systems of PDEs arising in problems within material sciences, propagation of waves, mean-field games, and imaging.