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

Fabrikant, I.; Karapetian, E.; Kalinin, S. V.

doi:10.1007/s00033-017-0894-5

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

Journal Article · Sat Dec 09 00:00:00 EST 2017 · Zeitschrift fuer Angewandte Mathematik und Physik

DOI:https://doi.org/10.1007/s00033-017-0894-5· OSTI ID:1426573

Fabrikant, I. ^[1]; Karapetian, E. ^[2]; Kalinin, S. V. ^[3]

Fabrikant-Research, Montreal, QC (Canada)
Suffolk Univ., Boston, MA (United States). Dept. of Mathematics and Computer Science
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Center for Nanophase Materials Science (CNMS)

Here, 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.

View Accepted Manuscript (DOE)

Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1426573

Alternate ID(s):: OSTI ID: 22860951

Journal Information:: Zeitschrift fuer Angewandte Mathematik und Physik, Journal Name: Zeitschrift fuer Angewandte Mathematik und Physik Journal Issue: 1 Vol. 69; ISSN 0044-2275

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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