Finite element modelling of crack tip behaviour in viscoelastic materials. Part I: Linear behaviour

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Abstract
A finite element algorithm which can be used to model either linear or non‐linear viscoelastic material behaviour is described. The algorithm is verified for the linear case by comparing numerical and analytical solutions for (a) a uniaxial tensile specimen, and (b) an infinite plate with a hole subjected to a remote uniaxial stress. The algorithm is then used to determine the stress and strain fields near the tip of a moving crack in a linear viscoelastic medium. Numerical solutions for both growing and healing cracks are compared with results expected based upon the extended correspondence principle. Excellent agreement between theoretical and numerical solutions is obtained in all cases. Sources of numerical error in the FE solution procedure are identified and documented. The algorithm has not been verified for the non‐linear case, since (except for very simple geometries and loading configurations) no closed‐form solutions involving non‐linear viscoelastic material behaviour are available. A comparison between the measured and predicted response of a non‐linear viscoelastic material behaviour will be presented in a following paper.