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Related Experiment Videos

Nonaffine correlations in random elastic media.

B A Didonna1, T C Lubensky

  • 1Institute for Mathematics and Its Applications, University of Minnesota, Minneapolis, Minnesota 55455-0436, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 21, 2006
PubMed
Summary

Materials with random elastic moduli exhibit nonaffine distortions under stress. The nonaffine displacement scales with the variance of these moduli, driven by spatial variations in elasticity, not random stress itself.

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Area of Science:

  • Solid Mechanics
  • Materials Science
  • Statistical Physics

Background:

  • Homogeneous materials respond affinely to stress, with linear displacement and constant strain.
  • Amorphous and heterogeneous materials possess spatially varying elastic moduli, leading to nonaffine distortions.

Purpose of the Study:

  • Investigate nonaffine response and correlation in materials with random elastic moduli.
  • Define and analyze nonaffine displacements and their correlation functions.
  • Identify the driving forces behind nonaffine distortions.

Main Methods:

  • Analytic calculations and numerical simulations.
  • Introduction of four model random systems with varying sources of elastic moduli randomness.
  • Analysis of nonaffinity correlation functions and related metrics.

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Main Results:

  • Nonaffine displacement scales with the variance of local elastic moduli, irrespective of the randomness origin.
  • The driving force for nonaffine displacements is the spatial derivative of the random elastic constant tensor multiplied by the affine strain.
  • Random stress alone does not induce nonaffine response, but its contribution to elastic moduli randomness does.

Conclusions:

  • Nonaffine distortions are a fundamental response in heterogeneous elastic materials.
  • The variance of elastic moduli is the key factor determining the magnitude of nonaffine displacements.
  • Understanding nonaffine response is crucial for predicting material behavior under stress.