Today’s 3D printers are likely to revolutionize personal fabrication, with their hardware improving everyday and their cost getting lower. In this walk, I will present my work in using 3D printers to replicate the appearance of objects. I will show that the base of using 3D printers effectively is the solution of complex optimization problems.
Time permitting, I will also introduce others’ work in this area.

Engineering, intended as the capability of producing innovation and new technology, pays an important tribute to mathematics. It is well known how the increasing computer power open the door to sophisticated models of physical and engineering systems. But there is much more in engineering for the use of mathematics. The word of new sensors, keeping information from the environment (airplanes, cars, industrial plants to the human body) for monitoring purposes to predict and prevent faults and dangerous scenarios through data signal processing, is one of the challenging opportunity. Special controls to realize new self-controlled devices or unmanned vehicles is another exciting example. Probabilistic models for optimizing the matching between technology performances and economics is another aspect of valuable importance.
The seminar aims to provide a glimpse on the use of advanced mathematics in the world of applications in industrial engineering, through concrete examples on running projects.

Graphene is a two-dimensional material with a unique set of properties, many of which rely on its planar two-dimensional structure. In many applications, graphene is supported on a substrate. Rather than a flatland, supported graphene describes a landscape shaped by out-of-plane features with different physical origins. Defects such as dislocations or grain boundaries can relax through out-of-plane deformations.
Gas trapped between graphene and the substrate can elastically deform graphene, producing blisters of various shapes and sizes. Lateral strain produced upon cooling after graphene synthesis invariably results in linear and localized wrinkles. Such wrinkles or bubbles locally modify the electronic properties and are seen as defects. It has been also suggested that the strong coupling between localized deformation and electronic structure could be harnessed in technology by strain engineering. Here, I will describe our efforts to understand the origin of elastic out-of-plane deformations in supported graphene, and to devise strategies to control deformation patterns.

The problem of an elastic rod deforming in a plane, namely the so-called ‘planar elastica’, has a long history, rooting to Jacob Bernoulli (1654-1705), Daniel Bernoulli (1700-1782), Leonhard Euler (1707-1783), and Pieter van Musschenbroek (1692-1761), but is still actual and rich of applications, sometimes unexpected. The elastica has attracted a great interest in the past and has involved contributions from first-class scientists, including Kirchhoff, Love, and Born. The research on the elastica marked the initiation of the calculus of variations and promoted the development of the theory of elliptic functions. Nowadays the elastica represents a useful introduction to the theory of nonlinear bifurcation and stability, but is also an important tool in the field of soft robotics and in the design of compliant mechanisms. Moreover, the elastica can be effectively used to explain snake or fish locomotion and to design snake-like robots.

In this talk, the theory of a planar, nonlinear elastic rod developed by Euler is used to present new phenomena in which nonlinearities (related to the fact that equilibrium of the rod is reached at large displacements) play a fundamental role.

Graphene, a carbon layer packed in a 2D honeycomb lattice, has been discussed theoretically in the 1940s, tough it took sixty years to be experimentally isolated in 2004. After ten years, as a result of its appealing electrical, mechanical and optical properties, graphene has driven an unexpected technological revolution. A snapshot of a variety of promising applications from flexible electronics to energy storage, to biomedical applications will be presented. The ongoing research is now driven by the control and the design of the structural and electronic graphene properties. Examples are: (i) the control of mobility (metal or insulator?) tailoring graphene nanoribbons, (ii) the control of charge transfer and lithium uptake for energy storage applications, as a function of graphene morphology, (iii) the enhancement of magnetic anisotropy with magnetic systems in contact with graphene. These recent experimental results are presented, looking forward further achievements on the ongoing graphene future technologies.

The unique electronic properties of graphene have attracted a huge amount of attention since its discovery in 2004. The structural properties of such a two-dimensional lattice are less known but not less exceptional. Graphene has a rippled structure at any finite temperature, negative lattice expansion, is elastic up to very large deformations but displays many anharmonic effects, has a peculiar phonon spectrum and melts in a very unusual way. The structural properties of graphene are rather well described by bond order classical potentials. We have shown in the past years that Monte Carlo simulations based on such a potential (LCBOPII) can provide a detailed picture of the structure of graphene and of the thermal long wavelength behaviour due to rippling and have compared our findings to continuum models developed to describe two-dimensional membranes . The advantage of classical simulations is the ability to deal with very large samples, allowing the study of localized (vacancies) and extended defects (grain boundaries), melting, strain and frictional behavior.  Examples will be shown in this talk.