University of Illinois Urbana-Champaign

Numerical Evaluation of Domain and Contour Integrals for Nonlinear Fracture Mechanics: Formulation and Implementation Aspects

Dodds, Robert H., Jr.; Vargas, P.M.

Content Files
SRS-542.pdf

Permalink

https://hdl.handle.net/2142/14167

Description

Title
Numerical Evaluation of Domain and Contour Integrals for Nonlinear Fracture Mechanics: Formulation and Implementation Aspects
Author(s)
  • Dodds, Robert H., Jr.
  • Vargas, P.M.
Issue Date
1988-08
Keyword(s)
  • Domain integrals
  • Contour integrals
  • Fracture mechanics
Date of Ingest
2009-11-04T23:39:28Z
Abstract
"The crack tip flux integral, denoted J, for local translations (Mode I) of a planar, curved crack front has potential application as a characterizing parameter in three-dimensional, nonlinear fracture mechanics. The integral, defined over a vanishingly small contour in a normal plane to the crack front, provides the pointwise value of the mechanical energy release rate. Arbitrary loading and material behavior are accommodated in the limit of a vanishing contour shrunk onto the crack front. Numerical evaluation of the integral in the context of finite element analysis necessarily leads to the development of computational procedures for non-vanishing, finite-sized contours. Such developments have proceeded along two lines with the corresponding introduction of ""Domain Integral"" (integrals over element volumes) and ""Contour Integral"" (line integrals and area integrals) methods. Each approach leads to identical numerical values; selection of a procedure thus becomes a matter of convenience in element meshing and problem specification. This report describes the theoretical basis of each computational procedure, associated numerical algorithms, and details of the implementation in the general purpose analysis system POLO-FINITE. Example problems addressing 2-D and 3-D cracked structures for linear and nonlinear response under thermomechanical loading are presented to illustrate the general applicability of the procedures."
Publisher
University of Illinois Engineering Experiment Station. College of Engineering. University of Illinois at Urbana-Champaign.
Series/Report Name or Number
Civil Engineering Studies SRS-542
Type of Resource
text
Genre of Resource
Technical Report
Language
en
Permalink
http://hdl.handle.net/2142/14167
Sponsor(s)/Grant Number(s)
David Taylor Research Center, Metals and Welding Division

Owning Collections

Civil Engineering Studies: Structural Research Series PRIMARY