I am a university lecturer and researcher working for a better understanding of the stability of structures and its consequences. Whether they are large or small, rigid or flexible, in a gravitational or electrostatic field, periodically repeating in space or in time, why is it they sometimes collapse and sometimes not? And do we want to prevent this loss of stability or make the best of it?

With the help of students and colleagues, maths, computers and model experiments, I strive to answer practical problems like the dynamics of imperfect rotating machineries or the large vibrations of electromechanical systems at the nano-scale, or more fundamental ones such as the relation between geometry and mechanics in slender elastic structures, or the stability of dynamical systems whose evolution function periodically vary in time or space.

Name: Arnaud Lazarus
Address: Sorbonne Université,
Faculté des Sciences et Ingénierie,
Institut Jean le Rond d'Alembert,
Tour 55-65, Bureau 511,
4 place Jussieu,
75252 Paris Cedex 05, France
Telephone: +33 01 44 27 25 59
E-mail: arnaud.lazarus(at)sorbonne-universite.fr

A curriculum Vitae, updated on 02/15/2021, can be downloaded [here].
ORCID, Google scholar or HAL profile.

Opened internship position at Institut d'Alembert:

Particle / elastic wave interactions:

with A. Abramian and S. Protière

When sand is sprinkled on a vibrated plate, it accumulates near the vibration nodes of the structure forming the famous “Chladni patterns” (see Figure top). These patterns, which vary with the forcing frequency, provide an easy visualization of a musical instrument when it needs to be tuned, for example. But what happens if the vibrating slender structure is soft enough, such as an elastic membrane or ribbon (see Figure bottom), so that particle/elastic wave interactions can no more be neglected. The proposed internship, mostly experimental, will consist in investigating those so-called soft Chladni experiments. We are looking for motivated and serious candidates at a master's level degree in mechanical engineering or applied physics. The project could be followed by a PhD thesis on a similar subject at Institut d'Alembert.

A brief proposal of this internship can be downloaded [here].

Topological imaging of buried defects:

with R. Cornaggia

Non-destructive evaluation (NDE) of a solid (e.g. a mechanical part or a part of the human body) aims at detecting and identifying defects that could be buried (cavities, fractures) wihtout deteriorating this solid. One particular method consists in measuring strains at the free surfaces of the solid when it is submitted to static or dyamical loads. Comparing these measurements to the expected reponse of a reference defect-free solid then enables to assert the presence or absence of defects. The goal of this internship is to characterize parallelepipedal silicone specimens in which known defects such as marbles or coins have been buried. Strain measurements will be peformed during quasi-static mechanical tests e.g. compression tests in several directions (see Figure). The focus of the internship will then be the implementation of a relevant identification method and its critical evaluation. This internship could be followed by a PhD thesis at Institut d'Alembert in Sorbonne Université, Paris.

A brief proposal of this internship can be downloaded [here]. Pour une version de la proposition en français, c'est [ici].

Rolling instabilities of elastic ribbons:

with S. Neukirch, F. Bertails-Descoubes, V. Romero

In the present project we want to model the dynamical instabilities of a rolling elastic ribbon in interaction with a support in the presence of friction. A first version of the modelling will be restricted to planar configurations, but 3D approaches involving torsion will then be developed. In parallel to the theoretical work, some experimental work is carried out by our team and comparison between the two approaches will be performed. These problems involve a mix of theoretical (buckling, bifurcation), modelling (variationnal formulation, dimensional reduction), and numerical (minimization under inequality constraints) approaches. Numerical work will involve path following, shooting techniques, finite element modelling, minimization and root solving, in Python, Mathematica, and C. These problems are also relevant to biological systems (such as the tank-treading instability of human red blood cells) or industrial applications (such as the standardized friction tests for rubber tires).

A brief proposal of this internship can be downloaded [here].