Localization of Adiabatic Deformations in Thermoviscoplastic Materials
Type
Conference PaperKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2018-06-27Online Publication Date
2018-06-27Print Publication Date
2018Permanent link to this record
http://hdl.handle.net/10754/628076
Metadata
Show full item recordAbstract
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.Sponsors
This research was supported by King Abdullah University of Science and Technology (KAUST).Publisher
Springer NatureConference/Event name
16th International Conference on Hyperbolic Problems: Theory, Numerics and Applications, 2016Additional Links
https://link.springer.com/chapter/10.1007%2F978-3-319-91548-7_21ae974a485f413a2113503eed53cd6c53
10.1007/978-3-319-91548-7_21