Research Statement

Interests, Objectives and Goals

A substantial part of my current and past research is concerned with smart materials and structures. Smart materials exploit a broad variety of physical mechanisms to modify their response in a manner that can be controlled through appropriate physical stimuli. Nature has been long using such adaptive structures in essentially all life forms. In contrast, human-made structures often appear inefficient, static, and cumbersome.

In particular, my research is addressed to smart structures as devices resulting from the combination of smart material behavior with slenderness. Beams, plates and shells are examples of slender structures, as they have one or two geometrical dimensions (thickness or cross-section diameter) negligible with respect to their principal size (length and/or width). Geometrical features such as slenderness allow displacements to be large with moderate involvement of strain, which in turn results into a greater potential of mechanical actuation.

The most common physical mechanisms exploited to achieve smart behavior are piezoelectricity and magnetostriction. Devices based on these principles are usually referred to as electro- or magneto-elastic. In particular, the use of a magnetic field to achieve actuation offers several advantages such as remote and contactless control, over other types of actuation, as well as the fact that it does not produce any polarization of the media nor chemical alteration. My most recent work in this direction is the development of theories of magnetoelastic beams composed of magneto-rheological elastomers. These are functional materials whose mechanical properties can be controlled upon the application of an external magnetic field by dispersing magnetic hard particles into a non-magnetic soft matrix. Such softness, when combined with slenderness, amplifies the overall deformation, giving rise to an effect called huge magnetostriction. At present, I am working on the optimal design of magnetic cantilevers to be used as actuators capable of complex motion patterns.

Material response can also be crafted to react to chemical stimuli. This is the case of gels, which have been within the focus of my most recent research. Gels are soft materials that can radically change their shape when swollen with a solvent. For these materials, photolithographic patterning of the cross-linking density of thin gel membranes and, more generally, the fabrication of composite thin gel structures enable three-dimensional transformations through non-homogeneous or anisotropic swelling.

This work has also motivated further interest in theories of species diffusion in solids, most notably, the Cahn–Hilliard system. Results of this line of research have been, among others, generalized theories of Cahn–Hilliard type which find their application in models for solid-state hydrogen-storage systems. For these systems I have contributed to the development of an analytical model to capture stress effects on the kinetics of hydrogen adsorption in nanoparticles, and to the development and analysis of PDE-based models to describe hysteresis in the absorption kinetics.

The non-linear, multi-physics, and three-dimensional character of theories of smart materials demands computationally intensive numerical methods which, when used alone, do not allow designers to gain insight about the key parameters and features that govern the response of these structures. This has motivated my research efforts to develop systematic methods to derive and justify dimensionally-reduced theories that can capture the mechanical behavior of thin structures with a minimal amount of mathematical complexity. These models allow engineers to gain insight from analytical or semi-analytical solutions, which are seldom found for three-dimensional models, and also to develop faster numerical approximation schemes. The derivation of structural theories is a nice example of sophistication turning into substantial simplification at the end of the journey.

Methods and Tools

The methods I use in my research are theoretical, although I have some collaboration with experimentalists. I draw mostly on tools from continuum mechanics with some ingredients from applied mathematics.

Continuum mechanics is that branch of mechanics which disregards the discrete nature of matter, treating a physical object as if a continuum collection of material points would fill its entire extent. What distinguishes continuum mechanics from related disciplines is the emphasis on systematic procedures that attempt to unify, as opposed to ad hoc constructions — an attitude that finds its roots in the Italian school of Rational Mechanics. Being an electrical engineer by training, it was the elegance and power of the methods of mechanics that drew me toward applications of structural theories to Micro-Electro-Mechanical Systems (MEMS), and from there to structural mechanics and mechanics of materials.

Applied mathematics provides a common language and a unified way to understand and solve problems arising in diverse sciences. Methods I have used include: asymptotic analysis, homogenization, and dimension reduction. The power of these methods lies in their ability to retain, in a mathematical model, the essential features and the essential physics.

Although it is not my main focus, I have also been able to carry out mathematical analysis of some of the models I have developed, with the most important results achieved in collaboration with leading experts in the field.

Collaborations

I regard the ability to interact with people from different backgrounds as an invaluable asset and a source of continual learning. My list of current and past coauthors includes: