MARCO MORANDOTTI - Assistant Professor at Politecnico di Torino - VARIATIONAL METHODS FOR MECHANICS ... AND SOMETHING MORE
The study of materials and their mechanical, physical, and chemical properties has challenged scientists in the last
centuries. The advances in modern Mathematics, including the theoretical developments and the computational
aspects, make it now possible to study models to describe the deformations of continuum bodies in various regimes.
Mathematical Analysis and Continuum Mechanics provide the right tools to build and study these models; in
particular, variational techniques are successfully used to minimise the energy associated with a deformation in
order to find the equilibrium configurations of a body subject to external forces.
In this seminar, Dr Morandotti will present some results concerning problems stemming from mechanics and
materials science that are successfully tackled with techniques from the calculus of variations. Specifically, he
will introduce some problems concerning dislocations in crystalline solids: it is important to study the motion
of dislocations and their effects when more and more of them are nucleated, to determine the alteration of the
mechanical properties of a defected body. He will then move to structured deformations, which were proposed
as a multi-scale mechanical theory that captures the contributions at the macroscopic level of both smooth and
non-smooth geometrical changes (disarrangements) at submacroscopic levels. In the framework of an energetic
formulation, structured deformations are a powerful tool to bridge mechanical responses at different length scales.
Dr Morandotti will show some results concerning energy relaxation and integral representation.
Finally, he will conclude by addressing a mean-field model for a system of distributed players whose strategies
evolve according to the replicator dynamics influenced by the players’ distribution: a strategy is either enhanced
or suppressed according to its performance with respect to the other available ones. The model, presented here
as a mean-field limit, besides recovering a discrete-to-continuum process similar to the one used for the upscaling
of dislocations, suggests applications to multi-particle dynamical systems.”
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