New concept of nonlocal continuum damage: Crack influence function

Zdenek P Bazant*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

The spatial averaging integral and weight function that have so far been employed in the macroscopic nonlocal models for strain-softening damage have been obtained by semi-intuitive arguments and justified by the need to limit damage localization in numerical computations. Some micromechanics arguments have recently also been presented, but microcrack interactions and growth have been neglected. The present conference paper gives a preliminary, abbreviated exposition of a new micromechanics analysis of a system of interacting and growing microcracks. The result is a new form of the spatial integral for nonlocal damage, in which the nonlocal stress field is a solution of a Fredholm integral equation over the neighborhood of a point. While in previous formulations the weight function has been assumed as a scalar, it is now found to be a tensor. Furthermore, the weight function is not axisymmetric (isotropic) but varies with the spherical angles (i.e., is anisotropic) and exhibits sectors of shielding and amplification. For long distances, the weight function decays as r-2 in two dimensions and as r-3 in three dimensions. Application of the Gauss-Seidel iteration method, which can be conveniently combined with iterations in each loading step of a nonlinear finite element code, simplifies the handling of the nonlocality since the nonlocal inelastic stress increments can be evaluated explicitly using directly the crack influence function. A detailed article is in preparation.

Original languageEnglish (US)
Title of host publicationMacroscopic Behavior of Heterogeneous Materials From the Microstructure
PublisherPubl by ASME
Pages153-160
Number of pages8
Volume147
ISBN (Print)0791811018
StatePublished - Dec 1 1992
EventWinter Annual Meeting of the American Society of Mechanical Engineers - Anaheim, CA, USA
Duration: Nov 8 1992Nov 13 1992

Other

OtherWinter Annual Meeting of the American Society of Mechanical Engineers
CityAnaheim, CA, USA
Period11/8/9211/13/92

ASJC Scopus subject areas

  • Mechanical Engineering

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  • Cite this

    Bazant, Z. P. (1992). New concept of nonlocal continuum damage: Crack influence function. In Macroscopic Behavior of Heterogeneous Materials From the Microstructure (Vol. 147, pp. 153-160). Publ by ASME.