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Inclusion Problem in Linear Viscoelastic Media

Kheirkhah Gildeh, Mohammad | 2020

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 52868 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Mohammad Shodja, Hossein
  7. Abstract:
  8. In this study, using the correspondence principle and Laplace transform, the results obtained in the elastic medium for the Eshelby inclusion problem are expanded into the linear viscoelastic medium. The simplicity and breadth of application of the correspondence principle is so great that it enables one to obtain closed-form solutions in Laplace domain for problems that have closed form solutions in elastic media. However, in complex problems, the long formulas lead the user to apply numerical methods to perform inverse Laplace transform. First, by taking advantage of Green’s function the strain and stress fields are obtained in Laplace domain for the points lying inside and outside of an arbitrary ellipsoidal inclusion embedded in an infinite viscoelastic matrix. Then, the Wolfram Mathematica software is used to convert the mentioned fields in Laplace domain into the time domain. In the next step, the equivalent inclusion method is used to generalize the inclusion problem to the inhomogeneity one. The goal is to find the time function of a particular stress component inside and outside of an ellipsoidal inhomogeneity made of glass which is embedded in a viscoelastic matrix and is subjected to uniform far-field stress. The time ranges from zero to 2000 hours. To understand the shape effect of the inhomogeneity on the stress, spheroidal, prolate spheroidal, oblate spheroidal, and fiber inhomogeneities are considered. The results are in full accordance with limiting elastic cases. To verify the results, the problems are modelled in ABAQUS. Comparing the analytical and numerical results reveals that the proposed method is accurate in computing stress function for the Eshelby inhomogeneity problem in linear viscoelastic media
  9. Keywords:
  10. Micromechanics ; Linear Vibration ; Inhomogeneity ; Green Function ; Eshelbi Method ; Eshelbi Inclusion Problem

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