Use of Ĵ-Integral in Dynamic Analysis of Cracked Linear Viscoelastic Solids by Finite-Element Method

[+] Author and Article Information
K. Kishimoto, S. Aoki, M. Sakata

Department of Physical Engineering, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo 152, Japan

J. Appl. Mech 49(1), 75-80 (Mar 01, 1982) (6 pages) doi:10.1115/1.3162074 History: Received March 01, 1981; Revised July 01, 1981; Online July 21, 2009


A computational method using the path (area)-independent Ĵ-integral is developed to analyze viscoelastic problems. Since the displacement field near the crack tip of a viscoelastic solid is dependent upon the complete past history of the dynamic stress-intensity factors, the Ĵ-integral is represented by a hereditary integral of the dynamic stress-intensity factors. We assume that the stress and strain rates vary in proportion to time during each increment of time and derive a formula to obtain the current value of the dynamic stress-intensity factor from the time increment of the Ĵ-value. Both pure and mixed mode problems of a suddenly loaded crack are analyzed by making use of the formula together with the conventional finite-element method. In order to demonstrate the capability and reliability of the present method, problems of a center crack and an oblique crack in viscoelastic rectangular plates are solved.

Copyright © 1982 by ASME
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