Interaction between a punch and an arbitrary crack or inclusion in a transversely isotropic half-space

Interaction between a punch and an arbitrary crack or inclusion in a transversely isotropic... We consider the problem of an arbitrary shaped rigid punch pressed against the boundary of a transversely isotropic half-space and interacting with an arbitrary flat crack or inclusion, located in the plane parallel to the boundary. The set of governing integral equations is derived for the most general conditions, namely the presence of both normal and tangential stresses under the punch, as well as general loading of the crack faces. In order to verify correctness of the derivations, two different methods were used to obtain governing integral equations: generalized method of images and utilization of the reciprocal theorem. Both methods gave the same results. Axisymmetric coaxial case of interaction between a rigid inclusion and a flat circular punch both centered along the z-axis is considered as an illustrative example. Most of the final results are presented in terms of elementary functions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Zeitschrift für angewandte Mathematik und Physik Springer Journals

Interaction between a punch and an arbitrary crack or inclusion in a transversely isotropic half-space

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Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Springer International Publishing AG, part of Springer Nature
Subject
Engineering; Theoretical and Applied Mechanics; Mathematical Methods in Physics
ISSN
0044-2275
eISSN
1420-9039
D.O.I.
10.1007/s00033-017-0894-5
Publisher site
See Article on Publisher Site

Abstract

We consider the problem of an arbitrary shaped rigid punch pressed against the boundary of a transversely isotropic half-space and interacting with an arbitrary flat crack or inclusion, located in the plane parallel to the boundary. The set of governing integral equations is derived for the most general conditions, namely the presence of both normal and tangential stresses under the punch, as well as general loading of the crack faces. In order to verify correctness of the derivations, two different methods were used to obtain governing integral equations: generalized method of images and utilization of the reciprocal theorem. Both methods gave the same results. Axisymmetric coaxial case of interaction between a rigid inclusion and a flat circular punch both centered along the z-axis is considered as an illustrative example. Most of the final results are presented in terms of elementary functions.

Journal

Zeitschrift für angewandte Mathematik und PhysikSpringer Journals

Published: Dec 9, 2017

References

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