Interaction between a punch and an arbitrary crack or inclusion in a transversely isotropic halfspace
Here, we consider the problem of an arbitrary shaped rigid punch pressed against the boundary of a transversely isotropic halfspace 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 zaxis is considered as an illustrative example. Most of the final results are presented in terms of elementary functions.
 Authors:

^{[1]};
^{[2]};
^{[3]}
 FabrikantResearch, 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)
 Publication Date:
 Grant/Contract Number:
 AC0500OR22725
 Type:
 Accepted Manuscript
 Journal Name:
 Zeitschrift fuer Angewandte Mathematik und Physik
 Additional Journal Information:
 Journal Volume: 69; Journal Issue: 1; Journal ID: ISSN 00442275
 Publisher:
 Springer
 Research Org:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING
 OSTI Identifier:
 1426573
Fabrikant, I., Karapetian, E., and Kalinin, S. V.. Interaction between a punch and an arbitrary crack or inclusion in a transversely isotropic halfspace. United States: N. p.,
Web. doi:10.1007/s0003301708945.
Fabrikant, I., Karapetian, E., & Kalinin, S. V.. Interaction between a punch and an arbitrary crack or inclusion in a transversely isotropic halfspace. United States. doi:10.1007/s0003301708945.
Fabrikant, I., Karapetian, E., and Kalinin, S. V.. 2017.
"Interaction between a punch and an arbitrary crack or inclusion in a transversely isotropic halfspace". United States.
doi:10.1007/s0003301708945. https://www.osti.gov/servlets/purl/1426573.
@article{osti_1426573,
title = {Interaction between a punch and an arbitrary crack or inclusion in a transversely isotropic halfspace},
author = {Fabrikant, I. and Karapetian, E. and Kalinin, S. V.},
abstractNote = {Here, we consider the problem of an arbitrary shaped rigid punch pressed against the boundary of a transversely isotropic halfspace 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 zaxis is considered as an illustrative example. Most of the final results are presented in terms of elementary functions.},
doi = {10.1007/s0003301708945},
journal = {Zeitschrift fuer Angewandte Mathematik und Physik},
number = 1,
volume = 69,
place = {United States},
year = {2017},
month = {12}
}
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