Department of Mathematical Sciences
 
Lucia Scardia

Senior Lecturer

4 West 3.45

Dept of Mathematical Sciences

Email: l.scardia@bath.ac.uk

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Lucia Scardia

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My research interests are in the calculus of variations, partial differential equations, and geometric measure theory, with applications in materials science. A unifying theme of my work is the rigorous derivation of upscaled models for complex materials starting from micro-scale models.

The focus of my current research is on dislocation theory. Dislocations are defects in the crystal structure of a metal, and they are considered the main responsible of the permanent deformation of metals at the macroscopic scale.

Bridging the scales between the well-understood models for dislocations at the level of the atomic lattice, and plasticity models at the the macroscopic, engineering scale is one of the big goals in materials science. This challenge has become the core of intensive research also in the mathematical community, for the central role it plays in understanding complex multiscale systems.

I find this challenge very intriguing and over the past five years my collaborators and I have made several contributions in this direction.

Other important areas where multiscale problems arise naturally include homogenisation of free discontinuity problems, nonlinear elasticity, dimension reduction, fracture mechanics and delamination.

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