The mechanical behaviour of granular materials depends on their grading. Crushing of particles under compression or shear modifies the grain size distribution, with a tendency for the percentage of fine material to increase.  It follows that the frictional properties of the material and the critical states are modified as a consequence of the changes in grain size distribution and the available range of packing densities.  The seminar will illustrate some problems connected with the selection of appropriate descriptors of particle shape (such as e.g., roundness, angularity, and roughness) and the results of an extended experimental investigation of the evolution of the grading of an artificial granular material, consisting of crushed expanded clay pellets under different loading conditions. The changes of grading of the material after isotropic, one-dimensional and constant mean effective stress triaxial compression are described using a single parameter based on the ratio of the areas under the current and an ultimate cumulative particle size distribution, which are both assumed to be consistent with self-similar grading with varying fractal dimension.  Relative breakage is related to the total work input for unit of volume.

According to Hund (1927) quantum mechanics forbids the existence of stable optically active (chiral) molecules as they violate the invariance under parity of the Hamiltonian. This paradox has attracted much attention ever since and there is not yet a universally accepted explanation. I will contend that spontaneous symmetry breaking provides a qualitative and quantitative explanation. A second puzzle concerning chiral molecules is homochirality in living matter. This means the almost uniform configuration of aminoacids and  sugars, left handed and  right handed respectively. I will suggest that spontaneous symmetry breaking and symmetry restoring phase transitions in non equilibrium may offer a clue to this problem.

It has been known for centuries that a body in contact with a substrate will start to slide only when the lateral force exceeds the static friction force. The transition from static to dynamic friction is not completely well defined, since even when the lateral force is below the nominal static friction, a body can slowly creep forward due to thermal activation. Furthermore, recent experiments indicate that frictional sliding occurs by the nucleation of detachment fronts at the contact interface that sometimes appear well before the onset of global sliding, calling into question our understanding of friction. These findings suggest that the onset of slip is due to microscopic processes, ultimately due to the interactions between individual atoms lying on the surfaces in contact, propagating up txo the macroscale to yield collective sliding.
In this lecture, I will first discuss the onset of slip at the nanoscale considering thermal activated creep of a Xe monolayer under a small external lateral force. In this conditions, slip proceeds by the nucleation and growth of
domains in the commensurate interface between the film and the substrate.
The results of numerical simulations can be understood by the classical theory of nucleation which allows to estimate the activation energy for creep.
At the macro-scale, the presence and evolution of frictional precursors is ruled by the interplay between elastic interactions and the sample geometry, leading to important effects that are not accounted for in traditional friction laws. I will thus discuss a three dimensional model for frictional slip that allows to quantitatively reproduce the spatio-temporal evolution of experimentally observed frictional precursors and provide predictions for geometries that have not yet been investigated. Our results could also be relevant better to understand slip precursors on earthquakes faults.

We will discuss the mechanical bases of cellular motility by swimming and crawling.
The photo, courtesy of A. Beran (OGS, Trieste), shows some Euglenids exhibiting "metaboly", a type of motion for which we have recently proposed a model.

Starting from observations of biological self-propulsion, we will analyze the geometric structure underlying motility at small scales,the swimming strategies available to microscopic swimmers, and recipes to optimize their strokes.

The lessons learned in the context of swimming motility will be then applied in the context of motility by crawling.
Our point of view is inspired by Geometric Control Theory. Implications for the design of engineered bio-inspired devices will be discussed.