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

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

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

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

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

Language

en

Permalink

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

Sponsor(s)/Grant Number(s)

David Taylor Research Center, Metals and Welding Division

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