PhD program in Biomedical Sciences - Annual report

Cycle: 				 Academical Year:  2023/24

PhD candidate: (Given name, Family name) 

Supervisor:						Co-Supervisor: (if applicable) 

(1000-1200 words with the current font and spacing; provide a title and think to this section as an Extended Abstract, so don’t provide too much background but rather focus on the relevant results achieved during the PhD year and on your progress toward the objectives of your dissertation; if relevant suggestions/critiques have been made by your evaluators, it may be nice to indicate how you addressed, or do you think to address, their points). The example below is real, authors are Basile Audoly and Sébastien Neukirch, Laboratoire de Modélisation en Mécanique, CNRS/Université Paris VI, 4 place Jussieu, Paris, France, Physical Review Letters (2005) DOI: 10.1103/PhysRevLett.95.095505). The problem of why spaghetti don’t break in half fascinated Richard Feynman, who (erroneously, it turns out) thought that the vibrations in the spaghetti caused it to split into three or more pieces; this paper uncovered the real reason. You may also want to look at https://www.youtube.com/watch?v=ADD7QlQoFFI.

Research summary: Fragmentation of Rods by Cascading Cracks: Why Spaghetti Does Not Break in Half

When thin brittle rods such as dry spaghetti pasta are bent beyond their limit curvature, they often break into more than two pieces, typically three or four. With the aim of understanding these multiple breakings, we study the dynamics of a bent rod that is suddenly released at one end. We find that the sudden relaxation of the curvature at this end leads to a burst of flexural waves, whose dynamics are described by a self-similar solution with no adjustable parameters. These flexural waves locally increase the curvature in the rod, and we argue that this counterintuitive mechanism is responsible for the fragmentation of brittle rods under bending. A simple experiment supporting the claim is presented.

The physical process of fragmentation is relevant to several areas of science and technology. Because different physical phenomena are at work during the fragmentation of a solid body, it has mainly been studied from a statistical viewpoint [1–5]. Nevertheless, a growing amount of works have included physical considerations: surface energy contributions [6], nucleation and growth properties of the fracture process [7], elastic buckling [8,9], and stress wave propagation [10]. Usually, in dynamic fragmentation, the abrupt application of fracturing forces (e.g., by an impact) triggers numerous elementary breaking processes, making a statistical study of the fragment sizes possible. This is in contrast to quasistatic fragmentation where a solid is crushed or broken at small applied velocities [11].

Here we consider such a quasistatic experiment whereby a stick of dry spaghetti is bent beyond its limit curvature. Most of the time, the pasta does not break in half but typically into three to ten pieces. This simple and intriguing experiment, which puzzled Feynman himself [12], remains unexplained to date. In this Letter, we explain this multiple failure process and point out a general mechanism of cascading failure in rods: a breaking event induces strong flexural waves that trigger other breakings, leading to an avalanchelike process. 

Let us consider a rod that is held at both ends and bent quasistatically with an increasing, uniform curvature. It breaks at time t = 0 when its curvature k0 reaches its limit value k*: a dynamic crack crosses the weakest section and breaks the rod into two halves. As the rod was initially bent with uniform curvature, the location of this first failure point is that of the strongest defect. We do not further discuss this initial breaking event, but instead focus on the subsequent dynamics of either half of the rod, for t > 0, and show that this dynamics generically leads to new breaking events at later times.

Since we are not interested in the statistics of the initial breaking event, we introduce and analyze throughout this Letter a model problem in which the release of a rod mimics the initial breaking event. Both problems indeed obey the same equations, but the advantage of the model problem is that the length L of the fragment is known in advance. In the model problem, the rod is initially uniformly bent and at rest. This is achieved by clamping one end and applying a moment M0 at the other end: M0 plays the role of the internal moment transmitted across the section that is about to fail; see Fig. 1. At time t = 0, this end is suddenly released as the applied moment M0 is removed instantaneously. The rod no longer is in equilibrium, and we study its subsequent dynamics.

The increase of curvature has thus been described analytically and was confirmed by a direct observation. We now focus on the long time behavior of released rods; see Fig. 3(d). Their delayed breaking is explained using the self-similar flexural wave (4), together with its reflections on the clamped end. [....] In Fig. 3(d), the rod ruptured at a distance s = 0.76L from the free end, at a time t = 6.7 ms after the release. From the period of free oscillations, we measured T=114 ms directly, hence a dimensionless fracture delay t/T = 58.5 x 10-3. By repeating the experiment [18], we found that the failure delay and its location along the rod vary. Failure appears to be extremely sensitive to the initial curvature  =0 (rods that are closer to their limit curvature tend to break sooner after release, hence closer to the released end) and probably also to the presence of defects. Twenty-five experiments were carried out with various pasta diameters (Barilla no. 1 with r1 = 0.57 mm and 1 = 0.521 m2/s; Barilla no. 5 with r5 = 0.84 mm and 5  = 0.735 m2/s; Barilla no. 7 with r7 = 0.95 mm and 7  = 0.82 m2/s) and initial curvatures (in the range 9.7–15.3 m-1), with L around 24 cm. All the breaking events collapse onto well-defined regions in a rescaled space-time diagram (s/L, t/T).

Publications (please indicate the articles that you published during the year covered by this report; your name should be underlined)

1. Rossini G, Puccini G, Verdi G (2015). On the flagship implications of authors’ order in scientific publications. Journal of Unlikely Results 5:132-135.
2. Verdi G, Puccini G, Rossini G (2016). A re-appraisal of flagship implications of authors’ order in scientific publications: new data and new evidences. Bulletin of Unlikely Results 5:245-248.

Conferences attended (Please follow the format below and underline your name).

1. Rossini G, Puccini G and Verdi G, There must be an easier way to make a living, ESEB 2015, XV meeting of the European Society for Experimental Biology (August 10-14 2015, Lausanne, Switzerland). International, Oral presentation.
2. Puccini G, Rossini G and Verdi G, Why did I get the second name? Biomedicine (September 21-25 2015, Roma, Italy). International, Poster.
3. Verdi G, Puccini G and Rossini G, On the art of recycling a dataset for congress communications, 76° Congresso della Unione Italiana Dottorandi (September 15-18 2015, Parma, Italy). National, Oral presentation.

Stays (please indicate periods in which you have been a visiting student in other labs; indicate the period of the stay, the name of the hosting scientist/lab and the name and country of the hosting Institution)

1. 17 Jan 2015 - 17 Feb 2015, Prof. Gary Carvalho, School of Biological Sciences. Bangor University (Bangor, UK)
2.  .......................