Young's modulus | EPFL Graph Search

Young's modulus E, the Young modulus, or the modulus of elasticity in tension or axial compression (i.e., negative tension), is a mechanical property that measures the tensile or compressive stiffness of a solid material when the force is applied lengthwise. It quantifies the relationship between tensile/compressive stress \sigma (force per unit area) and axial strain \varepsilon (proportional deformation) in the linear elastic region of a material and is determined using the formula: E = \frac{\sigma}{\varepsilon} Young's moduli are typically so large that they are expressed not in pascals but in gigapascals (GPa). Example:

Silly Putty (increasing pressure: length increases quickly, meaning low E)
Aluminium (increasing pressure: length increases slowly, meaning high E) Higher Young's modulus corresponds to greater (lengthwise) stiffness.

Although Young's modulus is named after the 1

"The Unbearable Lightness of the Cube": Using SMA to Express Lightness, Movement and Memory in Sculptures

Shape Memory Alloys (SMA) have been used in sculptures for quite some time. But only very few of these sculptures have gone on to earn wide recognition, mainly because the working conditions of the SMA must be carefully respected when sculptures are made. If they are not, the sculpture is bound to fail after a short time. Swiss artist Etienne Krahenbuhl was able to avoid such failure in his sculptures by maintaining a strong collaboration with Rolf Gotthardt, physicist at the EPFL (Ecole Polytechnique Federale de Lausanne). In his sculptures, the apparently low modulus of super-elastic material permits very smooth movement, and in a few cases the shape memory effect allows unexpected changes. In this paper, some of the results of a 9-year collaboration between the physicist and the sculptor will be shown.

Mcsc Asm International, Po Box 473, Novelty, Oh 44072-9901 Usa2008

Atomic force microscopy studies of nanotribology and nanomechanics

Ismaël Palaci

This thesis comes within the scope of tribology studies at the nanometer scale. The experimental techniques used in this work are essentially related to atomic force microscopy, which gives a direct access to the topography and forces of the studied systems. Two principal aspects of the nanotribology have kept our attention. They are the nanofriction and the nanomechanics. These two domains divide the thesis in two main parts that remain however intimately bound. The first experimental part of the thesis describes the friction of a nanoscopic tip sliding on hydrophilic surfaces. The dependence of the friction force on the sliding velocity is studied for various applied normal loads and surrounding relative humidity levels. We found a logarithmic dependence of the friction force on both the scanning velocity and the relative humidity. For the first time, a transition from a positive to a negative slope of the friction force versus the logarithm of the sliding velocity has been observed for the very same tip-surface contact, by varying the relative humidity. The role of the relative humidity on the friction force has then been studied more deeply, leading to a two-thirds power law dependence of the capillary force on the normal load. Finally, analytical expressions for the friction phenomenon and the capillary condensation between the asperities of the tip and the surface have been developed to explain the phenomenological behaviors. The second experimental part describes themechanics of carbon nanotubes and tobacco mosaic viruses. In order to stay in the linear elasticity regime, small indentation amplitudes have been applied in the radial direction of multiwalled carbon nanotubes adsorbed on a silicon oxide surface. Using a theory based on the Hertz model, the radial stiffness has been evaluated and compared to molecular dynamics simulations. We found a radial Young modulus strongly decreasing with increasing radius and reaching an asymptotic value of 30 ± 10 GPa. The tobacco mosaic viruses have been adsorbed on a polyimide porous membrane. Evidence for the softness of the viruses has been obtained by imaging the tubes with the atomic force microscope in non-contact mode. Viruses hanging like ropes over the pores of the surface served as basis to measure their bending Young modulus. Using a model of a clamped beam loaded by a discrete gradient of van der Waals forces, we found a bending Young modulus of 3.1 ± 0.1 MPa.

EPFL2007

Topology Optimization with Radial Basis Functions

Julien Hess

The purpose of this project is to perform topology optimization on the cantilever beam problem, which is a particular case of the two-dimensional elasticity problem. Based on a finite element discretization, a Matlab implementation of the elasticity problem is first presented. The Young modulus is then utilized in order to model the cavities in the beam. Finally, a topological optimization of the beam is performed by using a radial basis function approximation of the Young modulus.

2012

Atomic force microscopy studies of nanotribology and nanomechanics

Ismaël Palaci

EPFL2007