Loi de Hooke | EPFL Graph Search

En physique, la loi de Hooke modélise le comportement des solides élastiques soumis à des contraintes. Elle stipule que la déformation élastique est une fonction linéaire des contraintes. Sous sa forme la plus simple, elle relie l'allongement (d'un ressort, par exemple) à la force appliquée. Cette loi de comportement a été énoncée par le physicien anglais Robert Hooke en 1676. La loi de Hooke est en fait le terme de premier ordre d'une série de Taylor. C'est donc une approximation qui peut devenir inexacte quand la déformation est trop grande. Au-delà d'un certain seuil, la déformation peut aussi devenir permanente, ce qui invalide aussi la loi. En revanche, la loi de Hooke peut être considérée à toutes fins pratiques comme exacte quand les forces et les déformations sont suffisamment petites, aussi est-elle utilisée dans de très nombreux domaines de la physique et de l'ingénierie, tels que la séismologie, la mécanique moléculaire et l'acoustique. Loi de Hooke pour les ressorts

Modélisation mécanique de fils pour la simulation chirurgicale

Lindo Robert Duratti

Minimally Invasive Surgery (MIS) represents one of the major progresses in surgery in the last decade. In general, it is based on the application of small body-cuts through which instruments are inserted into the patient's body allowing the surgeon to carry out their job. The advantages are numerous, mainly related to the patient's health, and economic advantages. The rather small size of the necessary cuts means a decreased risk of trauma and a faster recovery. It follows that hospitalization time and costs are reduced significantly. The conditions in which such surgery takes place are considerably different from traditional surgery. First of all, the extent to which the surgical instruments may be moved freely is reduced, as they have to pass through a fixed point. Then, visualisation of the surgery site takes place on a computer screen. In laparoscopy, the screen is connected to a micro-camera whereas in interventional radiology, an image created by x-rays is displayed on the screen. As more new surgical techniques are continuously invented, it is expected that these techniques can be practiced by the surgeons and, more importantly, preferred by patients. Amongst these surgical techniques, the suturing during laparoscopic surgery requires a certain skill in instrument handling to realize the required knots. In interventional radiology, during an angiography, the manipulation of the catheter requires a highly trained hand as the catheter has to pass through a complex, 3-dimensional network of blood vessels. The catheter is only visible when a radio-opaque marker is injected while the patient is under the emission of x-rays. Furthermore, such pictures are 2D. To help the surgeons to improve their abilities, we propose a haptic simulator to learn how to realize the knots for the suturing and a virtual environment for the angiography. For both training modules, we developed a model of filament based on the Cosserat theory applied to one-dimensional structures, which can describe the behaviour of a string as well as the behaviour of a rigid and flexible rod (catheter). This model starts from the energetic formulation of the filament considering the Hook laws of continuum mechanics. The Lagrange equations provide us with the equations of motion which describe the model deformation. This model takes collisions and auto-collisions into account and it is revealed to be very efficient for interactive applications. The training module dedicated to angiography permits to carry out the most usual gesture: beside the catheter navigation, a marker can be injected to visualize the vessels, to drive the balloon angioplasty towards the pathology and to set stents. Moreover, the visual rendering is very realistic and the heart beatings as well as breathing are also simulated.

EPFL2008

A Real-Time Simulator for Interventional Radiology

Hannes Bleuler, Lindo Robert Duratti, Evren Samur, Fei Wang

Interventional radiologists manipulate guidewires and catheters and steer stents through the patient’s vascular system under X-ray imaging for treatment of vascular diseases. The complexity of these procedures makes trainingmandatory in order to master hand-eye coordination, instrument manipulation and procedure protocols for each radiologist. In this paper we present a simulator for interventional radiology, which deploys a model of guidewire/catheter based on the Cosserat theory applied to one-dimensional structures. This model starts from the energetic formulation of the filament considering the Hook laws of continuum mechanics. The Lagrange formulations are used to describe the model deformation. This model takes (self-) collisions into account and it is revealed to be very efficient for interactive applications. The simulation environment allows to carry out the most common procedures: guidewire and catheter navigation, contrast dye injection to visualize the vessels, balloon angioplasty and stent placement. Moreover, heartbeat as well as breathing are also simulated visually.

2008

Noncontacting benchtop measurements of the elastic properties of shales

Thomas Emmanuel Blum

We evaluated a laser-based noncontacting method to measure the elastic anisotropy of horizontal shale cores. Whereas conventional transducer data contained an ambiguity between phase and group velocity measurements, small laser source and receiver footprints on typical core samples ensured group velocity information in our laboratory measurements. With a single dense acquisition of group velocity versus group angle on a horizontal core, we estimated the elastic constants c11, c33, and c55 directly from ultrasonic waveforms, and c13 from a least-squares fit of modeled to measured group velocities. The observed significant P-wave velocity and attenuation anisotropy in these dry shales were almost surely exaggerated by delamination of clay platelets and microfracturing, but provided an illustration of the new laboratory measurement technique. Although challenges lay ahead to measure preserved shales at in situ conditions in the lab, we evaluated the fundamental advantages of the proposed method over conventional transducer measurements. © 2013 Society of Exploration Geophysicists.

2013

Modélisation mécanique de fils pour la simulation chirurgicale

Lindo Robert Duratti

EPFL2008