IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

The Implications of Rosen’s Experiment to Statistical Modeling and Methodology of Fibrous Composites

  • Oct. 21, 2013
  • 2 p.m.
  • LeConte 312

Abstract

Load-sharing systems are used to model fibrous composite materials. The modeling approach is based on some remarkable experiments conducted by Rosen (1964, 1965) on single layer unidirectional glass fiber composites under increasing tensile load. Rosen discovered that load could not be transferred through the composite matrix material around a fiber break beyond a distance he referred to as the ineffective length. The ineffective length is used to discretize the composite into a grid system of components for which the load-sharing is determined by a load-sharing rule.

In this talk we will discuss Rosen’s experiments, show how the grid conceptualization can be used (i) to estimate the component strength distribution from his photographs and (ii) to show that the composite strength distribution has a stress/strength (threshold mixture) distribution. We shall discuss how the mixture distribution can be used to get insights into the system structure. If time permits, we will also discuss how the behavior of the states of the components (failed/unfailed) in the grid system can be modeled as a Markov random field where the local structure of the field is quite simple. This facilitates the calculation of the Gibbs measure associated with the field.

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