Effective Elastic Moduli of Two-Dimensional Brittle Solids With Interacting Microcracks, Part I: Basic Formulations

[+] Author and Article Information
J. W. Ju, Tsung-Muh Chen

Department of Civil and Environmental Engineering, University of California, Los Angeles, CA 90024-1593

J. Appl. Mech 61(2), 349-357 (Jun 01, 1994) (9 pages) doi:10.1115/1.2901451 History: Received October 08, 1990; Revised July 22, 1992; Online March 31, 2008


Statistical micromechanical formulations are presented to investigate effective elastic moduli of two-dimensional brittle solids with interacting slit microcracks. The macroscopic stress-strain relations of elastic solids with interacting microcracks are micromechanically derived by taking the ensemble average over all possible realizations which feature the same material microstructural geometry, characteristics, and loading conditions. Approximate analytical solutions of a two-microcrack interaction problem are introduced to account for microcrack interaction among many randomly oriented and located microcracks. The overall elastic-damage compliances of microcrack-weakened brittle solids under uniaxial and biaxial loads are also derived. Therefore, stationary statistical micromechanical formulation is completed. Moreover, some special cases are investigated by using the proposed framework. At variance with existing phenomenological continuum damage models, the proposed framework does not employ any fitted “material parameters. ” “Cleavage 1” microcrack growth and “evolutionary damage models” within the proposed context will be presented in Part II of this series. It is emphasized that microstructural statistical informations are already embedded in the proposed ensemble-averaged equations and, therefore, no Monte Carlo simulations are needed.

Copyright © 1994 by The American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.






Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In