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Title: Scaling Symmetries in Elastic-Plastic Dynamic Cavity Expansion Equations Using the Isovector Method

Abstract

Cavity-expansion approximations are widely-used in the study of penetration mechanics and indentation phenomena. We apply the isovector method to a well-established model in the literature for elastic-plastic cavity-expansion to systematically demonstrate the existence of Lie symmetries corresponding to scale-invariant solutions. Here we use the symmetries obtained from the equations of motion to determine compatible auxiliary conditions describing the cavity wall trajectory and the elastic-plastic material interface. The admissible conditions are then compared with specific similarity solutions in the literature.

Authors:
 [1];  [1];  [1];  [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1407884
Report Number(s):
LA-UR-17-22262
Journal ID: ISSN 0033-5614
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Quarterly Journal of Mechanics and Applied Mathematics
Additional Journal Information:
Journal Volume: 71; Journal Issue: 1; Journal ID: ISSN 0033-5614
Publisher:
Oxford University Press
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Albright, Eric Jason, Ramsey, Scott D., Schmidt, Joseph H., and Baty, Roy S. Scaling Symmetries in Elastic-Plastic Dynamic Cavity Expansion Equations Using the Isovector Method. United States: N. p., 2017. Web. doi:10.1093/qjmam/hbx023.
Albright, Eric Jason, Ramsey, Scott D., Schmidt, Joseph H., & Baty, Roy S. Scaling Symmetries in Elastic-Plastic Dynamic Cavity Expansion Equations Using the Isovector Method. United States. doi:10.1093/qjmam/hbx023.
Albright, Eric Jason, Ramsey, Scott D., Schmidt, Joseph H., and Baty, Roy S. Sat . "Scaling Symmetries in Elastic-Plastic Dynamic Cavity Expansion Equations Using the Isovector Method". United States. doi:10.1093/qjmam/hbx023. https://www.osti.gov/servlets/purl/1407884.
@article{osti_1407884,
title = {Scaling Symmetries in Elastic-Plastic Dynamic Cavity Expansion Equations Using the Isovector Method},
author = {Albright, Eric Jason and Ramsey, Scott D. and Schmidt, Joseph H. and Baty, Roy S.},
abstractNote = {Cavity-expansion approximations are widely-used in the study of penetration mechanics and indentation phenomena. We apply the isovector method to a well-established model in the literature for elastic-plastic cavity-expansion to systematically demonstrate the existence of Lie symmetries corresponding to scale-invariant solutions. Here we use the symmetries obtained from the equations of motion to determine compatible auxiliary conditions describing the cavity wall trajectory and the elastic-plastic material interface. The admissible conditions are then compared with specific similarity solutions in the literature.},
doi = {10.1093/qjmam/hbx023},
journal = {Quarterly Journal of Mechanics and Applied Mathematics},
number = 1,
volume = 71,
place = {United States},
year = {2017},
month = {9}
}

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