IDEAS home Printed from
   My bibliography  Save this article

Unified physics of stretched exponential relaxation and Weibull fracture statistics


  • Mauro, John C.
  • Smedskjaer, Morten M.


The complicated nature of materials often necessitates a statistical approach to understanding and predicting their underlying physics. One such example is the empirical Weibull distribution used to describe the fracture statistics of brittle materials such as glass and ceramics. The Weibull distribution adopts the same mathematical form as proposed by Kohlrausch for stretched exponential relaxation. Although it was also originally proposed as a strictly empirical expression, stretched exponential decay has more recently been derived from the Phillips diffusion-trap model, which links the dimensionless stretching exponent to the topology of excitations in a glassy network. In this paper we propose an analogous explanation as a physical basis for the Weibull distribution, with an ensemble of flaws in the brittle material serving as a substitute for the traps in the Phillips model. One key difference between stretched exponential relaxation and Weibull fracture statistics is the effective dimensionality of the system. We argue that the stochastic description of the flaw space in the Weibull distribution results in a negative dimensionality, which explains the difference in magnitude of the dimensionless Weibull modulus compared to the stretching relaxation exponent.

Suggested Citation

  • Mauro, John C. & Smedskjaer, Morten M., 2012. "Unified physics of stretched exponential relaxation and Weibull fracture statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 6121-6127.
  • Handle: RePEc:eee:phsmap:v:391:y:2012:i:23:p:6121-6127
    DOI: 10.1016/j.physa.2012.07.013

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    As the access to this document is restricted, you may want to search for a different version of it.


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Sarabia, José María & Prieto, Faustino & Trueba, Carmen & Jordá, Vanesa, 2013. "About the modified Gaussian family of income distributions with applications to individual incomes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1398-1408.

    More about this item


    Glass; Relaxation; Fracture statistics; Theory;


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:391:y:2012:i:23:p:6121-6127. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.