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.
Fabrikant, I., et al. "Interaction between a punch and an arbitrary crack or inclusion in a transversely isotropic half-space." Zeitschrift fuer Angewandte Mathematik und Physik, vol. 69, no. 1, Dec. 2017. https://doi.org/10.1007/s00033-017-0894-5
Fabrikant, I., Karapetian, E., & Kalinin, S. V. (2017). Interaction between a punch and an arbitrary crack or inclusion in a transversely isotropic half-space. Zeitschrift fuer Angewandte Mathematik und Physik, 69(1). https://doi.org/10.1007/s00033-017-0894-5
Fabrikant, I., Karapetian, E., and Kalinin, S. V., "Interaction between a punch and an arbitrary crack or inclusion in a transversely isotropic half-space," Zeitschrift fuer Angewandte Mathematik und Physik 69, no. 1 (2017), https://doi.org/10.1007/s00033-017-0894-5
@article{osti_1426573,
author = {Fabrikant, I. and Karapetian, E. and Kalinin, S. V.},
title = {Interaction between a punch and an arbitrary crack or inclusion in a transversely isotropic half-space},
annote = {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.},
doi = {10.1007/s00033-017-0894-5},
url = {https://www.osti.gov/biblio/1426573},
journal = {Zeitschrift fuer Angewandte Mathematik und Physik},
issn = {ISSN 0044-2275},
number = {1},
volume = {69},
place = {United States},
publisher = {Springer},
year = {2017},
month = {12}}
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 99, Issue 7https://doi.org/10.1002/zamm.201800319
Journal Article
·
Sat Jan 31 23:00:00 EST 1987
· Journal of Heat Transfer (Transcations of the ASME (American Society of Mechanical Engineers), Series C); (United States)
·OSTI ID:5403678