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

A computational method using the path (area)-independent Jˆ-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 Jˆ-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 Jˆ-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.