gamma-convergence

Asymptotic properties of composites

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B9 L2 R2322 H1

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.

Part 1: Introduction to homogenisation and Gamma-Convergence

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B2 B3 A0215

We will start by introducing the notion of Gamma-convergence and its main properties. We will then show how this can be applied to the study of homogenization of integral functionals. This includes, as a particular case, the homogenization of uniformly elliptic PDEs. Lecture 1: (1) The homogenisation problem; (2) Gamma-convergence - definition, main properties, examples, comparison with pointwise limit; (3) Lower semicontinuity, lower semicontinuous envelope; (4) Coercivity

Part 2: Introduction to homogenisation and Gamma-Convergence

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B1 L2 R2202

We will start by introducing the notion of Gamma-convergence and its main properties. We will then show how this can be applied to the study of homogenization of integral functionals. This includes, as a particular case, the homogenization of uniformly elliptic PDEs. Lecture 2: (1) Integral functionals with p growth, 1 p 1; The localisation method of Gamma-convergence; Integral representation.

Part 3: Introduction to homogenisation and Gamma-Convergence

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B1 L4 R4214

We will start by introducing the notion of Gamma-convergence and its main properties. We will then show how this can be applied to the study of homogenization of integral functionals. This includes, as a particular case, the homogenization of uniformly elliptic PDEs. Lecture 3: (1) Compactness; (2) Application of the compactness result; 93) The homogenisation theorem.

Rita A. Ferreira

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