Localization of Adiabatic Deformations in Thermoviscoplastic Materials

Files
shbndhyp2016.pdf (213.97 KB)

Type
Conference Paper

Authors
Lee, Min-Gi
Katsaounis, Theodoros
Tzavaras, Athanasios

KAUST Department
Applied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Online Publication Date
2018-06-27

Print Publication Date
2018

Date
2018-06-27

Abstract
We study an instability occurring at high strain-rate deformations, induced by thermal softening properties of metals, and leading to the formation of shear bands. We consider adiabatic shear deformations of thermoviscoplastic materials and establish the existence of a family of focusing self-similar solutions that capture this instability. The self-similar solutions emerge as the net response resulting from the competition between Hadamard instability and viscosity. Their existence is turned into a problem of constructing a heteroclinic orbit for an associated dynamical system, which is achieved with the help of geometric singular perturbation theory.

Citation
Lee M-G, Katsaounis T, Tzavaras AE (2018) Localization of Adiabatic Deformations in Thermoviscoplastic Materials. Springer Proceedings in Mathematics & Statistics: 269–280. Available: http://dx.doi.org/10.1007/978-3-319-91548-7_21.

Acknowledgements
This research was supported by King Abdullah University of Science and Technology (KAUST).

Publisher
Springer Nature

Journal
Theory, Numerics and Applications of Hyperbolic Problems II

Conference/Event Name
16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016

DOI
10.1007/978-3-319-91548-7_21

Additional Links
https://link.springer.com/chapter/10.1007%2F978-3-319-91548-7_21

Permanent link to this record
http://hdl.handle.net/10754/628076
Collections
Conference Papers
Applied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division