Mechanical Behavior of the Lamellar Structure in Semi-Crystalline Polymers

We have employed molecular dynamics simulations to study the behavior of virtual polymeric materials under an applied uniaxial tensile load. Through computer simulations, one can obtain experimentally inaccessible information about phenomena taking place at the molecular and microscopic levels. Not only can the global material response be monitored and characterized along time, but the response of macromolecular chains can be followed independently if desired. The computer-generated materials were created by emulating the step-wise polymerization, resulting in self-avoiding chains in 3D with controlled degree of orientation along a certain axis. These materials represent a simplified model of the lamellar structure of semi-crystalline polymers,being comprised of an amorphous region surrounded by two crystalline lamellar regions. For the simulations, a series of materials were created, varying i) the lamella thickness, ii) the amorphous region thickness, iii) the preferential chain orientation, and iv) the degree of packing of the amorphous region. Simulation results indicate that the lamella thickness has the strongest influence on the mechanical properties of the lamella-amorphous structure, which is in agreement with experimental data. The other morphological parameters also affect the mechanical response, but to a smaller degree. This research follows previous simulation work on the crack formation and propagation phenomena, deformation mechanisms at the nanoscale, and the influence of the loading conditions on the material response. Computer simulations can improve the fundamental understanding about the phenomena responsible for the behavior of polymeric materials, and will eventually lead to the design of knowledge-based materials with improved properties.

Unknown Radial Distortion Centers in Multiple View Geometry Problems

The radial undistortion model proposed by Fitzgibbon and the radial fundamental matrix were early steps to extend classical epipolar geometry to distorted cameras. Later minimal solvers have been proposed to find relative pose and radial distortion, given point correspondences between images. However, a big drawback of all these approaches is that they require the distortion center to be exactly known. In this paper we show how the distortion center can be absorbed into a new radial fundamental matrix. This new formulation is much more practical in reality as it allows also digital zoom, cropped images and camera-lens systems where the distortion center does not exactly coincide with the image center. In particular we start from the setting where only one of the two images contains radial distortion, analyze the structure of the particular radial fundamental matrix and show that the technique also generalizes to other linear multi-view relationships like trifocal tensor and homography. For the new radial fundamental matrix we propose different estimation algorithms from 9,10 and 11 points. We show how to extract the epipoles and prove the practical applicability on several epipolar geometry image pairs with strong distortion that - to the best of our knowledge - no other existing algorithm can handle properly.