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Structural Monitoring and Maintenance
  Volume 8, Number 1, March 2021 , pages 111-124

Continuously inhomogeneous beam structure with creep: a longitudinal crack study
Victor I. Rizov

    The main purpose of the present paper is to evaluate the influence of increase of the coefficient of viscosity with time on the strain energy release rate for a longitudinal crack in a continuously inhomogeneous beam configuration under linear creep. The beam exhibits continuous material inhomogeneity along the width, thickness and length. The creep behavior is studied analytically by a viscoelastic model structured by one dashpot and three springs. The coefficient of viscosity of the dashpot and the modulii of elasticity of the springs are distributed continuously in the width, thickness and length directions of the beam. Besides, the coefficient of viscosity increases with time. Time-dependent solutions to the strain energy release are derived by considering the balance of the energy and by applying the compliance method. The results obtained by the two solutions are identical which proves the correctness of the analysis performed. The solutions take into account the creep behavior and the increase of the coefficient of viscosity with time. A parametric study of the strain energy release rate is carried-out by using the solutions derived. It is found that the strain energy release rate decreases with increasing of the coefficient of viscosity with time.
Key Words
    longitudinal crack; beam structure; viscoelastic behavior; creep; continuous material inhomogeneity
Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy, 1 Chr. Smirnensky blvd., 1046 — Sofia, Bulgaria.

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